Dataset Viewer
messages
listlengths 1
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| groundtruth
stringlengths 1
79.2M
| dataset
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values | data_source
stringclasses 10
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dict | split
stringclasses 2
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|---|---|---|---|---|---|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "In the expansion of $(2x-\\frac{1}{x})^{5}$, calculate the coefficient of $x$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
80
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given the function $f(x)=\\frac{a\\ln x}{x}+b\\ (a,b\\in\\mathbb{R})$, its graph has a tangent line at the point $(1,f(1))$ with the equation $y=x-1$.\n\n(I) Find the values of the real numbers $a$ and $b$ and the monotonic intervals of the function $f(x)$;\n\n(II) Compare $x\\_1+x\\_2$ with $2e\\ (e$ is the base of the natural logarithm$)$ when $f(x\\_1)=f(x\\_2)\\ (x\\_1\\neq x\\_2)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
x\_1+x\_2>2e
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "The slope of the line $2x+2y-5=0$ is what angle?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
135^{\circ}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given the function $f(x)=\\ln(x-1)-k(x-1)+1$ $(k\\in \\mathbb{R})$.\n\n$(1)$ Find the intervals of monotonicity for the function $f(x)$;\n\n$(2)$ If $g(x)=\\frac{1}{3}x^3-\\ln(x+1)+f(x+2)$ satisfies: for any $x_1, x_2 \\in [0,1]$, $|g(x_1)-g(x_2)|\\leqslant 1$ always holds, determine the range of the real number $k$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
-\frac{2}{3}\leqslant k\leqslant \frac{4}{3}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given the hyperbola _\\\\(C\\\\)_: \\\\(\\dfrac{x^2}{a^2} - \\dfrac{y^2}{b^2} = 1\\\\) (_\\\\(a > 0\\\\)_, _\\\\(b > 0\\\\)_) with its right vertex at _\\\\(A\\\\)_, a circle with center _\\\\(A\\\\)_ and radius _\\\\(b\\\\)_ is drawn, intersecting one of the asymptotes of the hyperbola _\\\\(C\\\\)_ at points _\\\\(M\\\\)_ and _\\\\(N\\\\)_. If \\\\(∠MAN = 60^\\circ\\\\), then the eccentricity of _\\\\(C\\\\)_ is _______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\dfrac{2\sqrt{3}}{3}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given a parabola $y^2 = 2px$ ($p > 0$) with focus $F$, let $A$ and $B$ be two moving points on the parabola such that $\\angle AFB = 60^\\circ$. Let $M$ be the midpoint of $AB$, and draw a perpendicular line $MN$ from $M$ to the parabola's axis, with foot $N$. Find the maximum value of $\\frac{|MN|}{|AB|}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
1
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "If circle $C_{1}: x^{2}+y^{2}=1$ is tangent to circle $C_{2}: x^{2}+y^{2}-6x-8y+m=0$, then the value of the real number $m$ is ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
9
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Calculate the value of the expression $\\lg 5^{2}+ \\dfrac{2}{3} \\lg 8+ \\lg 5 \\cdot \\lg 20+ (\\lg 2)^{2}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
3
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given the function $f(x)=a(x+1)^{2}-4\\ln x$, where $a\\in\\mathbb{R}$. \n(Ⅰ) If $a= \\frac {1}{2}$, find the equation of the tangent line to the curve $f(x)$ at the point $(1,f(1))$; \n(Ⅱ) If for any $x\\in[1,e]$, $f(x) < 1$ always holds, find the range of the real number $a$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
(-\infty, \frac {1}{4})
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Six geologists, named A, B, C, D, E, and F, are to be assigned to four different high schools, A, B, C, and D, with each high school having at least one geologist. Calculate the total number of different ways to make the assignments.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
1560
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Compute the value of $\\cos 80^{\\circ}\\cos 20^{\\circ}+\\sin 80^{\\circ}\\sin 20^{\\circ}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\dfrac{1}{2}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "If $5a^{|x|}b^2$ and $-0.2a^3b^{|y|}$ are like terms, determine the values of $x$ and $y$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
±2
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Select 3 TV sets from 4 Type A and 5 Type B TV sets, such that among the selected 3, there is at least one TV of each type. Calculate the total number of different selection methods.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
70
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given a tetrahedron P-ABC where AB=AC=1, AB⊥AC, PA⊥ the plane ABC, and the tangent of the angle formed by line PA and plane PBC is 1/2, find the volume of the circumscribed sphere of the tetrahedron P-ABC.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{4\pi}{3}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "For the algebraic expression in terms of $x$, $\\left(ax-3\\right)\\left(2x+1\\right)-4x^{2}+m$, after simplification, it does not contain the terms $x^{2}$ and constant term. Given that $an+mn=1$, where $an+mn=1$, find the value of $2n^{3}-9n^{2}+8n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{157}{125}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given two complex numbers $z_1 = a + i$ ($a \\in \\mathbb{R}$), $z_2 = 1 - i$, and $\\frac{z_1}{z_2}$ is a pure imaginary number, determine the quadrant in which the point corresponding to $z_1$ lies on the complex plane.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
1
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Let $\\vec{a} =(m,\\sin 2x)$ and $\\vec{b} =(\\cos 2x,n)$ where $x\\in \\mathbb{R}$, and let $f(x)= \\vec{a}\\cdot \\vec{b}$. The graph of $f(x)$ passes through the points $(0,1)$ and $\\left( \\frac{\\pi}{4} ,1\\right)$.\n\n$(1)$ Find the analytic expression of $f(x)$; \n$(2)$ If $x\\in \\left[0, \\frac{\\pi}{2}\\right]$, find the maximum and minimum values of $f(x)$ and the corresponding values of $x$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{\pi}{2}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given $$( \\frac {a}{x}- \\sqrt {x})^{6}(a＞0)$$, the constant term in its expansion is 60. \n(1) Find $a$; \n(2) Find the coefficient of the term containing $$x^{ \\frac{3}{2}}$$; \n(3) Find all rational terms in the expansion; \n(4) Find the term with the largest coefficient and the term with the largest binomial coefficient in the expansion.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
-960x^{- \frac {3}{2}}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "The equation of the tangent line to the curve $y=4x-x^3$ at the point $(-1, -3)$ is.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
x-y-2=0
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given the function $f(x)=\\frac{1}{3} x^{3}+x^{2}-2ax+1$, if the function $f(x)$ has an extreme value in the interval $(1,2)$, then the range of the real number $a$ is \\_\\_\\_\\_\\_\\_\\_\\_.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\left( \frac{3}{2},4\right)
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given the function f(x) = sin(2x + $\\frac{\\pi}{4}$), where x belongs to the interval [$\\frac{\\pi}{4}$, $\\frac{\\pi}{2}$], determine the range of f(x).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
[- \frac{\sqrt{2}}{2}, \frac{\sqrt{2}}{2}]
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given that $\\overrightarrow {m}$=（cosα，sinα） and $\\overrightarrow {n}$=（ $\\sqrt {3}$，-1）, where α∈（0，π）.\n(1) If $\\overrightarrow {m}$ is perpendicular to $\\overrightarrow {n}$, find the value of angle α.\n(2) Find the minimum value of $|$ $\\overrightarrow {m}$+ $\\overrightarrow {n}$$|$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
1
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "In the expansion of $\\left(\\frac{1}{\\sqrt{x}} - 3\\right)^n$ (where $n \\in \\mathbb{N}^*$), the sum of all the coefficients is 16. Find the coefficient of $\\frac{1}{x}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
54
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given the function $f(x)=4+a^{x-1}$, the coordinates of point $P$ through which the graph of the function always passes are $\\_\\_\\_\\_\\_\\_\\_.$\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
(1, 5)
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "The number of sets $A$ that satisfy $\\left\\{ 1 \\right\\} \\subseteq A \\subset \\left\\{ 1,2,3 \\right\\}$ is ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
3
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "The range of the function $f(x)=\\frac{2}{{x-1}}, x∈[2,6]$\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
[\frac{2}{5}, 2]
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "A conference room is illuminated by 3 lamps, each using one energy-saving bulb of the same model. Assuming whether each lamp can illuminate normally only depends on the lifespan of the bulb, the probability that the lifespan of this model of bulb exceeds 1 year is 0.8, and the probability that the lifespan exceeds 2 years is 0.3. Bulb replacement is carried out annually, only replacing those that have failed, without replacing any that are still working. \n(I) During the first bulb replacement, calculate the probability of not needing to replace any bulbs and the probability of needing to replace 2 bulbs; \n(II) During the second bulb replacement, for one of the lamps, calculate the probability that the bulb needs to be replaced.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
0.6
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "If $m$ and $n$ are reciprocals of each other, then the value of $mn^2 - (n - 3)$ is $\\_\\_\\_\\_\\_\\_$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
3
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "The coordinates of the focus of the parabola $y^2 = 20x$ must be determined.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
(5, 0)
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Let the universal set $U = \\{1,2,3,4,5\\}$, $M = \\{1,4\\}$, and $N = \\{1,3,5\\}$. Find the intersection of $N$ and the complement of $M$ in $U$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\{3,5\}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given that $S_n$ is the sum of the first $n$ terms of an arithmetic sequence $\\{a_n\\}$, and $a_2=2, S_9=45$. Let $b_n=\\left[\\lg a_n\\right]$, where $\\left[x\\right]$ denotes the greatest integer less than or equal to $x$, such as $\\left[ 0.1 \\right]=0, \\left[ \\lg 11 \\right]=1$. Then, the sum of the first $1,001$ terms of the sequence $\\{b_n\\}$ is __________.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
1896
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given the sets $M=\\{x|x-1=0\\}$ and $N=\\{x|x^2-3x+2=0\\}$, determine the intersection of sets $M$ and $N$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\{1\}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given the function $f(x)=\\sin^{2}x+\\sqrt{3}\\sin x\\sin (x+\\frac{\\pi}{2})$.\n\n1. Find the value of $f(\\frac{\\pi}{12})$;\n2. Find the maximum and minimum values of the function $f(x)$ when $x\\in[0,\\frac{\\pi}{2}]$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{3}{2}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given the function $y=-6\\sin^2\\left(x+\\frac{\\pi}{6}\\right)+3$, transform it into the function $y=-3\\cos 2x$ by a suitable transformation and specify the direction and magnitude of the horizontal shift.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
-\frac{\pi}{3}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given $x+y=1$, $x>0$, $y>0$, calculate the minimum value of $\\frac{1}{2x}+\\frac{x}{y+1}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{5}{4}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given that $a$ and $b$ are positive real numbers, and $a+b=1$, find the minimum value of $\\frac{1}{a} + \\frac{1}{b}$ and the corresponding value of $a$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{1}{2}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "In a geometric sequence $\\{a_n\\}$ where each term is positive, if $a_3a_5=4$, determine the sum of the first 7 terms of the sequence $\\{\\log_2 a_n\\}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
7
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Suppose the deficient approximate value and excess approximate value of $\\pi$ are $\\frac{31}{10}$ and $\\frac{16}{5}$, respectively, and after the first application of the \"Tiao Ri Method\" yields $\\frac{16}{5}$ as a more precise excess approximate value of $\\pi$. If we always use the simplest fraction, find the approximate fraction that can be obtained after the fourth application of the \"Tiao Ri Method\".\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{22}{7}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "In acute triangle $\\triangle ABC$, if $\\sin A= \\frac {3}{5}$, $AB=5$, $AC=6$, then $BC=$ \\_\\_\\_\\_\\_\\_ .\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\sqrt {13}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "The sum of the first \\\\(n\\\\) terms of the sequence \\\\(1 \\dfrac{1}{3}, 2 \\dfrac{1}{9}, 3 \\dfrac{1}{27}, 4 \\dfrac{1}{81}, \\ldots\\\\) is \\_\\_\\_\\_\\_\\_.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\dfrac{n^2+n+1}{2} - \dfrac{1}{2\cdot 3^n}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given $i$ as the imaginary unit, find the modulus $|z|$ of the complex number $z=(1-i)(1+i)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
2
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given points $A(-1,3)$ and $B(3,-1)$, find the slope angle of line $AB$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
135^{o}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Let point $P$ be any point on the circle $x^{2}+y^{2}=4$, and let the fixed point $D$ have coordinates $(8,0)$. When point $P$ moves on the circle, the equation of the trajectory of the midpoint $M$ of segment $PD$ is ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
(x-4)^{2}+y^{2}=1
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given vectors $\\overrightarrow {OA} = (k,12,1)$, $\\overrightarrow {OB} = (4,5,1)$, $\\overrightarrow {OC} = (-k,10,1)$, and points A, B, C are collinear, find the value of k.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{2}{3}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Read the material: Find the value of $1+2+2^{2}+2^{3}+2^{4}+\\ldots +2^{2017}$. \nSolution: Let $S=1+2+2^{2}+2^{3}+2^{4}+\\ldots +2^{2017}$, multiply both sides of the equation by $2$ simultaneously: \n$2S=2+2^{2}+2^{3}+2^{4}+2^{5}+\\ldots +2^{2018}$ \nSubtract the above equation from the previous one: $2S-S=2^{2018}-1$, which means $S=2^{2018}-1$ \nTherefore, $1+2+2^{2}+2^{3}+2^{4}+\\ldots +2^{2017}=2^{2018}-1$ \nPlease calculate the following using the same method: \n$(1)1+2+2^{2}+2^{3}+2^{4}+\\ldots +2^{10}$ \n$(2)1+3+3^{2}+3^{3}+3^{4}+\\ldots +3^{2016}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{3^{2017} - 1}{2}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "The solution to the one-variable linear equation $\\frac{x+1}{3}=0$ with respect to $x$ is ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
x = -1
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Solve the following questions:\n(1) Given $\\cos(\\alpha+\\beta)= \\frac{1}{3}$ and $\\cos(\\alpha-\\beta)= \\frac{1}{5}$, find the value of $\\tan\\alpha\\tan\\beta$;\n(2) Given $\\theta \\in \\left[0, \\frac{\\pi}{4}\\right]$, and $\\sin^4\\theta + \\cos^4\\theta = \\frac{5}{8}$, find the value of $\\sin\\theta\\cos\\theta$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{\sqrt{3}}{4}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Express the phrase \"twice of $x$ plus one third of $y$\" in algebraic form.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
2x + \frac{1}{3}y
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Simplify $\\sin 10^{\\circ}\\cos 50^{\\circ}+\\cos 10^{\\circ}\\sin 50^{\\circ}=$ \\_\\_\\_\\_\\_\\_.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\dfrac { \sqrt {3}}{2}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "If line $l$ is symmetric to the line $x+y-1=0$ with respect to the y-axis, then the equation of line $l$ is.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
x-y+1=0
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Let the modulus of the complex number $a+bi$ ($a,b \\in \\mathbb{R}$) be $\\sqrt{3}$. Then, the value of $(a+bi)(a-bi)$ is \\_\\_\\_\\_\\_\\_\\_\\_\\_.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
3
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "The opposite of $2023$ is what value?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
-2023
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given that $f(x) = ax^2+bx+2$ is an even function defined on the interval $[1+a, 2]$, find the range of $f(x)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\text{The range of } f(x) \text{ is } [-10, 2]
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "In $\\triangle ABC$, it is known that $a=2$, $A=120^{\\circ}$. Find the radius of the circumcircle of $\\triangle ABC$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac {2\sqrt {3}}{3}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given the geometric sequence \\\\(\\{a_n\\}\\\\), \\\\(a_4=2\\\\) and \\\\(a_5=5\\\\), find the sum of the first \\\\(8\\\\) terms of the sequence \\\\(\\{\\lg a_n\\}\\\\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
4
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Let the common ratio of a geometric sequence with positive terms $\\{a_n\\}$ be $q$, and $\\frac {S_{3}}{a_{3}}=7$, then the common ratio $q=$ \\_\\_\\_\\_\\_\\_.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac {1}{2}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "In the Cartesian coordinate system, the coordinates of point $A(-5,2)$ with respect to the point $B$ that is symmetric about the $y$-axis are ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
(5,2)
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Convert the binary number $101 101_2$ to its decimal equivalent.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
45
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Calculate the following expressions:\n1. $(1)(\\frac{27}{8})^{-\\frac{2}{3}} - (\\frac{49}{9})^{0.5} + (0.008)^{-\\frac{2}{3}} \\times \\frac{2}{25}$\n2. $(2)\\log_{10} 25 + \\frac{2}{3} \\log_{10} 8 + \\log_{10} 5 \\cdot \\log_{10} 20 + (\\log_{10} 2)^2$\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
3
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Throwing a fair die, the probability of any number appearing on the top face is $\\dfrac{1}{6}$. Let event $A$ be \"the number on the top face is odd\", and event $B$ be \"the number on the top face is no more than $3$\". Then, the probability $P(A\\cup B)=$ .\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\dfrac{2}{3}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given that the complex number $z$ and $(z-3)^2+5i$ are both purely imaginary, then $z= \\_\\_\\_\\_\\_\\_$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\pm3i
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "If the polynomial $3(a^{2}-2ab-b^{2})-(a^{2}+mab+2b^{2})$ with respect to $a$ and $b$ does not contain the term $ab$, then $m=\\_\\_\\_\\_\\_\\_$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
-6
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "In the rectangular coordinate system $(xOy)$, the parametric equations of the curve $C\\_1$ are given by $\\begin{cases} x=2+2\\cos \\phi \\\\ y=2\\sin \\phi \\end{cases}$ ($\\phi$ is the parameter). Establish a polar coordinate system with the origin $O$ as the pole and the positive half of the $x$-axis as the polar axis. The polar equation of the curve $C\\_2$ is given by $\\rho=4\\sin \\theta$.\n(I) Find the Cartesian equation of $C\\_1$ and the polar equation of $C\\_2$.\n(II) Given that the polar equation of the curve $C\\_3$ is $\\theta=\\alpha$ ($0 < \\alpha < \\pi$, $\\rho\\in \\mathbb{R}$), point $A$ is the intersection of curves $C\\_3$ and $C\\_1$, point $B$ is the intersection of curves $C\\_3$ and $C\\_2$, and both points $A$ and $B$ are distinct from the origin $O$ with $|AB|=4\\sqrt{2}$, find the value of $\\alpha$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\alpha=\frac{3\pi}{4}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given the line $x-2y+a=0$ and the circle $(x-2)^{2}+y^{2}=1$, determine the range of values for the real number $a$ such that these two have common points.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
[-2-\sqrt{5}, -2+\sqrt{5}]
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "The equation of the tangent line to the curve $y=\\sin x + e^x$ at the point $(0,1)$ is \\_\\_\\_\\_\\_\\_.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
y = 2x + 1
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given the function $f(x) = x^{3} - x^{2} + ax + 1$. \n$(1)$ Discuss the monotonicity of $f(x)$. \n$(2)$ Find the coordinates of the point where the tangent line passing through the origin intersects the curve $y = f(x)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
(-1, -a - 1)
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given the function $f(x)=|x-a|+ \\frac{1}{2a}$ (where $a\\neq 0$), \n(1) If the inequality $f(x)-f(x+m)\\leqslant 1$ always holds, find the maximum value of the real number $m$; \n(2) When $a < \\frac{1}{2}$, the function $g(x)=f(x)+|2x-1|$ has a zero, determine the range of the real number $a$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
[-\frac{1}{2}, 0)
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given the line $l_1: ax-y-2=0$ passes through the center of the circle $C: (x-1)^2+y^2=1$.\n\n(1) Find the value of $a$; \n(2) Find the equation of the line $l_2$ that passes through the center of the circle $C$ and is parallel to the line $l: x-4y+1=0$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
x-4y-1=0
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given that $f(x)$ is an odd function defined on $[-1,1]$, if $m, n \\in [-1,1]$ and $m+n \\neq 0$, then $\\frac{f(m)+f(n)}{m+n} > 0$. Determine the solution set for the inequality $f(x+\\frac{1}{2}) < f(1-x)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
[0,\frac{1}{4})
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given the sequence $\\{a_n\\}$ with the general term $a_n= \\begin{cases} n+ \\frac {15}{n}, & n\\leqslant 5 \\\\ a\\ln n- \\frac {1}{4}, & n > 5\\end{cases}$, if the minimum value of $\\{a_n\\}$ is $\\frac {31}{4}$, then the range of the real number $a$ is ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\left[ \frac {8}{\ln 6},+\infty\right)
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Express the solution set of the inequality $|x-1| < 1$ in interval notation.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
(0,2)
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given $x > -1$, the value of $x$ corresponding to the minimum value of the function $$y=x+ \\frac {1}{x+1}$$ is \\_\\_\\_\\_\\_\\_.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
0
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "In the geometric sequence $\\{a_n\\}$, $a_3=4$, $a_7=12$, find the value of $a_{11}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{12^2}{4} = 36
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given that $n\\in\\mathbb{N}^+$, find the value of $\\frac {1}{2!}+ \\frac {2}{3!}+\\ldots+ \\frac {n}{(n+1)!}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
1 - \frac {1}{(n+1)!}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given that the sequence $\\{{a_{n} }\\}$ is an arithmetic sequence with a common difference of $0$, and ${a_{1}}=1$, ${a_{1} }$, ${a_{3} }$, ${a_{6} }$ form a geometric sequence, find the sum of the first $n$ terms, $S_n$, of the sequence $\\{{a_{n} }\\}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\dfrac {n^{2}}{8}+ \dfrac {7n}{8}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Let $\\triangle ABC$ have side lengths $a$, $b$, $c$ opposite to angles $A$, $B$, $C$ respectively. Given that the area of the triangle is $\\sqrt{3}$, $B=60^{\\circ}$, and $a^{2}+c^{2}=3ac$, find $b$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
2\sqrt{2}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "During the Spring Festival in 2023, in order to further leverage the positive role of e-commerce in the active consumer market and ensure that the people spend a safe, healthy, happy, and peaceful Chinese New Year, Company A and Company B simultaneously launched discount promotions and live streaming activities with New Year goods on a certain shopping platform. Company A and Company B sell similar products and compete with each other. \n$(1)$ Now, a survey was conducted on the shopping choices of 100 viewers who watched the live streams of these two companies during a certain period of time, and the following data was obtained: \n\n| | Choose Company A | Choose Company B | Total |\n|-------------------|------------------|------------------|-------|\n| Age 19-24 years | 40 | 10 | 50 |\n| Age 25-34 years | 20 | 30 | 50 |\n| Total | 60 | 40 | 100 |\n\nCan we be $99.9\\%$ certain that the choice of shopping in which live stream room is related to the user's age? \n$(2)$ If Xiao Li chooses to shop in one of the live stream rooms of Company A or Company B for two consecutive days, and on the first day, he equally likely chooses one of the two live stream rooms for shopping, with a probability of $0.7$ to shop in Company A's live stream room on the second day if he shopped there on the first day, and a probability of $0.8$ to shop in Company A's live stream room on the second day if he shopped in Company B's live stream room on the first day, what is the probability that Xiao Li will shop in Company B's live stream room on the second day? \n$(3)$ During New Year's Day, Company A's shopping platform live stream room conducted a \"flash sale\" activity. Assuming that the probability of each person successfully placing an order in the live stream room is $p (0<p<1)$, and the success or failure of each person's order is independent. If five people are randomly selected from the live stream room, and the probability of exactly $2$ people successfully placing an order among the five people is denoted as $f(p)$, find the maximum point $p_{0}$ of $f(p)$. \nReference formula: $K^{2}=\\frac{n(ad-bc)^{2}}{(a+b)(c+d)(a+c)(b+d)}$, where $n=a+b+c+d$. \nCommon small probability values and corresponding critical values in $K^{2}$ independence test table: \n\n| $P(K^{2}\\geqslant k)$ | $0.10$ | $0.05$ | $0.01$ | $0.005$ | $0.001$ |\n|-----------------------|--------|--------|--------|---------|---------|\n| $k$ | $2.706$| $3.841$| $6.635$| $7.879$ | $10.828$|\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{2}{5}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given the following definition: We call a pair of rational numbers $a$ and $b$ that satisfy the equation $a-b=ab+1$ as \"companion rational number pairs,\" denoted as $\\left(a,b\\right)$. For example, $3-\\frac{1}{2}=3\\times \\frac{1}{2}+1$, $5-\\frac{2}{3}=5\\times \\frac{2}{3}+1$, so the pairs $(3,\\frac{1}{2})$ and $(5,\\frac{2}{3})$ are both \"companion rational number pairs.\"\n\n$(1)$ Among the pairs $(-2,\\frac{1}{3})$ and $(-\\frac{1}{2},-3)$, the \"companion rational number pair\" is ______;\n\n$(2)$ If $\\left(x+1,5\\right)$ is a \"companion rational number pair,\" then the value of $x$ is ______;\n\n$(3)$ If $\\left(a,b\\right)$ is a \"companion rational number pair,\" find the value of $3ab-a+\\frac{1}{2}(a+b-5ab)+1$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{1}{2}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given an arithmetic sequence $\\{a_n\\}$ with the sum of its first $n$ terms denoted as $S_n$, $a_2=4$, and $S_{10}=110$, determine the minimum value of $\\frac{S_n+64}{a_n}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{17}{2}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Express 1.14 billion in scientific notation.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
1.14 \times 10^9
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given that in right triangle $ABC$, $\\angle ACB=90^{\\circ}$ and $AB=3$, calculate the value of $AB^{2}+BC^{2}+AC^{2}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
18
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Calculate using a simple method: $-\\frac{1}{8}-(+1\\frac{1}{3})-(-\\frac{5}{8})-(+4\\frac{2}{3})$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
-5\frac{1}{2}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given that the equation of line $l$ is $\\frac{x}{2}+\\frac{y}{2}=1$, find the slope angle $\\alpha$ of line $l$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
135^{\circ}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "The height of a cylinder is 8 cm, and its surface area is $130\\pi \\text{ cm}^2$. The radius of its base circle is \\_\\_\\_\\_\\_\\_ cm.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
5
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "The shortest distance from a point on the line $y=x-1$ to the circle $x^2+y^2+4x-2y+4=0$ is ______.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
2\sqrt{2} - 1
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given that $U = \\mathbb{R}$, the solution set to the inequality $ax^2 + 2x + b > 0 (a \\neq 0)$ is $\\{x | x \\neq -\\frac{1}{a}, x \\in \\mathbb{R}\\}$, and $a > b$, find the set of all possible values of $t = \\frac{a^2 + b^2}{a-b}$. Let set $B = \\{m | |x+1| - |x-3| \\leq m^2 - 3m, x \\in \\mathbb{R}\\}$ always holds true. Determine $A \\cap (\\complement_U B)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
[2\sqrt{2}, 4)
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "In an experiment, four sets of values for the pair \\\\((x,y)\\\\) are measured as \\\\(A(1,2)\\\\), \\\\(B(2,3)\\\\), \\\\(C(3,5)\\\\), and \\\\(D(4,6)\\\\).\n\n\\\\((\\\\)Ⅰ\\\\()\\\\) Try to find the regression line equation between \\\\(y\\\\) and \\\\(x\\\\), \\\\( \\hat{y}=bx+a\\\\);\n\n\\\\((\\\\)Ⅱ\\\\()\\\\) Use the regression line equation to predict the value of \\\\(y\\\\) when \\\\(x=5\\\\).\n\n\\\\((b= \\dfrac { \\sum\\limits_{i=1}^{n}(x_{i}- \\overline {x})(y_{i}- \\overline {y})}{ \\sum\\limits_{i=1}^{n}(x_{i}- \\overline {x})^{2}}= \\dfrac { \\sum\\limits_{i=1}^{n}x_{i}y_{i}-n \\overline {x} \\overline {y}}{ \\sum\\limits_{i=1}^{n} x_{ i }^{ 2 }-n \\overline {x}^{2}},a= \\overline {y}-b \\overline {x})\\\\)\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
7.5
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given the sequence $\\{a_n\\}$, $a_1=2$, and $a_{n+1}=a_n+ \\frac {2}{n(n+1)}$ for all $n \\in \\mathbb{N}^*$, calculate the value of $a_{10}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{19}{5}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given the proposition $p$: \"The equation $x^{2}+mx+1=0$ has two real roots\"; and the proposition $q$: \"$\\forall x \\in \\mathbb{R}$, $4x^{2}+4(m-2)x+1 \\neq 0$\", if $p \\wedge q$ is false, and $\\neg q$ is false, find the range of values for the real number $m$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
(1, 2)
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "In triangle $\\triangle ABC$, $BC=\\sqrt{7}$, $AC=2\\sqrt{3}$, $A=\\frac{π}{6}$, then the length of $AB$ is ____.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
AB=5 \text{ or } AB=1
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "The imaginary part of the complex number $\\frac{{3+4i}}{{3-4i}}$ is ____.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{24}{25}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "A TV station is broadcasting 6 advertisements in succession, which include 3 different commercial advertisements, 2 different promotional advertisements, and 1 public service advertisement. The last advertisement played must not be a commercial advertisement, and the promotional advertisements cannot be played consecutively, nor can they be played consecutively with the public service advertisement. How many different play orders are possible?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
6 + 6 + 6 = 18
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Let $f(x)=\\log_{2}(\\frac{1}{x}+a)$, where $a\\in \\mathbb{R}$. <br/> $(1)$ When $a=2$, find the solution set of the inequality $f(x) < 2$; <br/> $(2)$ When $a > 0$, if for any $t\\in [\\frac{1}{2}, 1]$, the difference between the maximum and minimum values of the function $f(x)$ on the interval $[t, t+1]$ does not exceed $1$, find the range of values for $a$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
[\frac{2}{3}, +\infty)
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given the system of linear equations in two variables $x$ and $y$: $\\left\\{\\begin{array}{l}2x-y=4m-5\\\\x+4y=-7m+2\\end{array}\\right.$, where the solutions satisfy $x+y \\gt -3$, and $m$ is a non-negative integer, find the value of $m$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
m=0 \text{ or } m=1
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Find the coordinates of a point $C$ such that it lies on the same line with points $A(-1,1,0)$ and $B(-1,0,1)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
(-1, \frac{1}{2}, \frac{1}{2})
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given that the terminal side of angle $\\alpha$ passes through point $P(-8m, -6\\sin 30^{\\circ})$, and $\\cos \\alpha = -\\frac{4}{5}$, find the value of $m$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{1}{2}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given that the sequence $\\{a\\_n\\}$ is an arithmetic sequence with the sum of the first $n$ terms denoted as $S\\_n$, and $a\\_3=6$, $S\\_3=12$.\n\n(I) Find $a\\_n$;\n\n(II) Find the sum of the first $n$ terms of the sequence $\\{a\\_n\\}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
n(n+1)
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given $a^2 + a - 3 = 0$, calculate the value of $a^2(a + 4)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
9
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "In the sequence $\\{a_n\\}$, $a_1=1$, $a_{n+1}=2a_n+1$, then the general formula for $a_n$ is $a_n=\\ $.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
2^n-1
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
[
{
"content": [
{
"content": "\nWhen tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.\n\n[ASSESS]\n\n[ADVANCE]\n\n[VERIFY]\n\n[SIMPLIFY]\n\n[SYNTHESIZE]\n\n[PIVOT]\n\n[OUTPUT]\n\nYou should strictly follow the format below:\n\n[ACTION NAME]\n\n# Your action step 1\n\n# Your action step 2\n\n# Your action step 3\n\n...\n\nNext action: [NEXT ACTION NAME]\n\n",
"role": "system"
},
{
"content": "Given that $\\sin 2\\alpha = \\frac {24}{25}$, with $0 < \\alpha < \\frac {\\pi}{2}$, find the value of $\\sqrt {2}\\cos\\left(\\frac {\\pi}{4} - \\alpha\\right)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac {7}{5}
|
math
|
numina_cn_k12
|
{
"index": 0,
"split": "dummy"
}
|
train
|
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