Dataset Viewer
messages
listlengths 1
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| groundtruth
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435
| dataset
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value | extra_info
dict | split
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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": "Determine the residue of $-1234 \\pmod{32}$. Your answer should be an integer in the range $0,1,2,\\ldots,30,31$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
14
|
math
|
numina_synthetic_math
|
{
"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": "What is the remainder when 7645 is divided by 9?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
4
|
math
|
numina_synthetic_math
|
{
"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 $7 \\times 10$ rectangle is used to form two different cylindrical shapes by rolling it along its length and width. Calculate the ratio of the larger volume to the smaller volume when the rectangle is formed into cylinders in these two ways. Express your answer as a common fraction.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{10}{7}
|
math
|
numina_synthetic_math
|
{
"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 $C_n$ be the sum of the first $n$ terms of the geometric series\n\\[ 512 + \\frac{512}{4} + \\frac{512}{16} + \\dotsb, \\]\nand let $D_n$ be the sum of the first $n$ terms of the geometric series\n\\[ 3072 - \\frac{3072}{3} + \\frac{3072}{9} - \\dotsb. \\]\nCalculate the smallest integer value of $n \\ge 1$ for which $C_n = D_n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
1
|
math
|
numina_synthetic_math
|
{
"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 all real values of $x$ that satisfy \\[\\frac{1}{x^2+1} > \\frac{4}{x} + \\frac{25}{10}.\\] (Give your answer in interval notation.)\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
(-2, 0)
|
math
|
numina_synthetic_math
|
{
"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 the expression \\( y - 3(2+y) + 4(2-y^2) - 5(2+3y) \\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
-4y^2 - 17y - 8
|
math
|
numina_synthetic_math
|
{
"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 roots of the quadratic equation $2x^2 + 16x + c = 0$ are $x = \\frac{-16 \\pm \\sqrt{24}}{4}$, what is the value of $c$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
29
|
math
|
numina_synthetic_math
|
{
"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 \\(a,\\) \\(b,\\) and \\(c\\) be positive real numbers such that \\(abc = 8.\\) Find the minimum value of\n\\[(a + 3b)(b + 3c)(ac + 2).\\]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
64
|
math
|
numina_synthetic_math
|
{
"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": "What is the $30^\\text{th}$ triangular number?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
465
|
math
|
numina_synthetic_math
|
{
"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 $\\mathbf{A} = \\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix}$ and $\\mathbf{B} = \\begin{pmatrix} x & y \\\\ z & w \\end{pmatrix}$ be two matrices such that $\\mathbf{A}^T = \\mathbf{A}^{-1}$ and $\\mathbf{B}^T = \\mathbf{B}^{-1}$. If $\\mathbf{C} = \\mathbf{A} \\mathbf{B}$, find the value of $x^2 + y^2 + z^2 + w^2$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
2
|
math
|
numina_synthetic_math
|
{
"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 polynomial equation \\[x^4 + dx^2 + ex + f = 0,\\] where \\(d\\), \\(e\\), and \\(f\\) are rational numbers, has \\(3 - \\sqrt{5}\\) as a root. It also has two integer roots. Find the fourth root.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
-7
|
math
|
numina_synthetic_math
|
{
"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 ray of light passing through point \\(A = (-2, 10, 12)\\), reflects off the plane \\(x + y + z = 14\\) at \\(B\\), and then passes through the point \\(C = (4, 3, 7)\\). Find the point \\(B\\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\begin{pmatrix} 4 \\ 3 \\ 7 \end{pmatrix}
|
math
|
numina_synthetic_math
|
{
"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 rectangular room measuring 15 feet by 20 feet is to be covered with tiles each measuring 3 inches by 9 inches. How many tiles are required to cover the entire floor?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
1600
|
math
|
numina_synthetic_math
|
{
"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 $\\overline{AB}$ be a diameter of circle $\\omega$. Extend $\\overline{AB}$ through $A$ to $C$. Point $T$ lies on $\\omega$ such that line $CT$ is tangent to $\\omega$. Point $P$ is the foot of the perpendicular from $A$ to line $CT$. Suppose $\\overline{AB} = 16$, and let $m$ denote the maximum possible length of segment $BP$. Find $m^{2}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
320
|
math
|
numina_synthetic_math
|
{
"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 solutions to $z^6 = -8.$ Enter the solutions, separated by commas.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\pm (1+i), \pm (1-i), \pm \sqrt[6]{-8}
|
math
|
numina_synthetic_math
|
{
"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 $g(x) = (x-3)^2 + 1$. If the domain of $g$ is all real numbers, then $g$ does not have an inverse function. However, if we restrict the domain of $g$ to an interval $[c,\\infty)$, then $g$ may have an inverse function. What is the smallest value of $c$ we can use here so that $g$ does have an inverse function?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
3
|
math
|
numina_synthetic_math
|
{
"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 number is chosen at random from the set of consecutive natural numbers $\\{1, 2, 3, \\ldots, 60\\}$. What is the probability that the number chosen is a factor of $5!$? Express your answer as a common fraction.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{4}{15}
|
math
|
numina_synthetic_math
|
{
"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 degree measure of the least positive angle $\\theta$ for which\n\\[\\sin 15^\\circ = \\cos 40^\\circ + \\cos \\theta.\\]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
115^\circ
|
math
|
numina_synthetic_math
|
{
"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 play has three different male roles, two different female roles, and one role that can be either gender. Only a man can be assigned to a male role, and only a woman can be assigned to a female role. If six men and five women audition, in how many ways can the six roles be assigned?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
14400
|
math
|
numina_synthetic_math
|
{
"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": "Determine the largest integer $m$, such that $m$ is a multiple of 18, and every digit of $m$ is either 6 or 9. Then find the value of $\\frac{m}{18}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
53872
|
math
|
numina_synthetic_math
|
{
"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 regular hexagon $ABCDEF$, diagonal $AD$ is drawn. Given that each interior angle of a regular hexagon measures 120 degrees, calculate the measure of angle $DAB$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
30
|
math
|
numina_synthetic_math
|
{
"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": "From the set of integers $\\{1,2,3,\\dots,3000\\}$, choose $k$ pairs $\\{a_i, b_i\\}$ with $a_i < b_i$ so that no two pairs share a common element. Suppose all the sums $a_i + b_i$ are distinct and less than or equal to $3000$. Find the maximum possible value of $k$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
899
|
math
|
numina_synthetic_math
|
{
"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 largest value of $c$ such that $-2$ is in the range of $f(x) = x^2 + 4x + c$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
2
|
math
|
numina_synthetic_math
|
{
"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 arithmetic mean of an even number of consecutive odd integers is $z$. Find the sum of the smallest and largest of the integers in terms of $z$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
2z
|
math
|
numina_synthetic_math
|
{
"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": "Centered at each lattice point in the coordinate plane are a circle radius $\\frac{1}{8}$ and a square with sides of length $\\frac{1}{4}$ whose sides are parallel to the coordinate axes. The line segment from $(0,0)$ to $(1009, 437)$ intersects $m$ of the squares and $n$ of the circles. Find $m + n$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
526
|
math
|
numina_synthetic_math
|
{
"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 all $x$ such that $x^2 + 5x < 10$. Express your answer in interval notation.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
(-5, 2)
|
math
|
numina_synthetic_math
|
{
"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 library storage room, there are $1500$ boxes, each containing $45$ books.\n\nJanet is tasked to reorganize the books such that each new box contains $47$ books. After Janet repacks the books into as many full boxes as possible, how many books does she have left over?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
13
|
math
|
numina_synthetic_math
|
{
"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 $x^2 + y^2 = 16x + 8y + 8$, find the largest possible value of $4x + 3y$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
63
|
math
|
numina_synthetic_math
|
{
"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": "What is the sum of the first 15 even positive integers?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
240
|
math
|
numina_synthetic_math
|
{
"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": "How many integers between $100$ and $999$ have three different digits in strictly decreasing order?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
120
|
math
|
numina_synthetic_math
|
{
"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 point $(4,-5)$ is on the graph of $y=g(x)$, and $h(x)=(g(x))^2 + 3$ for all $x$, then there is one point that must be on the graph of $y=h(x)$. What is the sum of the coordinates of that point?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
32
|
math
|
numina_synthetic_math
|
{
"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": "Consider a cube with an edge length of 2 units. This cube is cut similarly to the original problem to form several pieces. What is the volume of the piece that contains vertex $W$, if the piece is a pyramid with a rectangular base having sides of lengths 1 unit and 2 units, and with the altitude (W to the base) at 1 unit?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{2}{3}
|
math
|
numina_synthetic_math
|
{
"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": "Determine the remainder when the sum $7283 + 7284 + 7285 + 7286 + 7287$ is multiplied by 2 and then divided by 9.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
0
|
math
|
numina_synthetic_math
|
{
"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 roots of the equation $3x^2 - 8x - 5 = 0$ can be written in the form $x = \\frac{m \\pm \\sqrt{n}}{p}$, where $m$, $n$, and $p$ are positive integers with a greatest common divisor of 1. What is the value of $n$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
124
|
math
|
numina_synthetic_math
|
{
"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 product of all possible values for $a$ if the length of the segment between the points $(2a, a-4, a+2)$ and $(4, -1, 3)$ is $3\\sqrt{5}$ units.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{-19}{6}
|
math
|
numina_synthetic_math
|
{
"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": "Evaluate the expression $|(7 + 6i)(-5 + 3i)|$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\sqrt{2890}
|
math
|
numina_synthetic_math
|
{
"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": "What is the first digit (from left to right) of the base $9$ representation of $582_{10}$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
7
|
math
|
numina_synthetic_math
|
{
"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 $f(1)=5$, $f(2)=8$, and $f(x) = ax^2 + bx + 2$. Find the value of $f(3)$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
11
|
math
|
numina_synthetic_math
|
{
"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 two positive integers is 72 and their difference is 18. Calculate the product of these two integers.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
1215
|
math
|
numina_synthetic_math
|
{
"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": "Lines $m$ and $n$ are parallel, and the measure of $\\angle 1$ is $\\frac{1}{6}$ the measure of $\\angle 2$. If $\\angle 3$ is equal in measure to $\\angle 1$, and $\\angle 2$ and $\\angle 4$ form a straight line, what is the degree measure of $\\angle 5$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{180^\circ}{7}
|
math
|
numina_synthetic_math
|
{
"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": "When $n$ is divided by 4, the remainder is 3. What is the remainder when $7n$ is divided by 4?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
1
|
math
|
numina_synthetic_math
|
{
"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": "What is the remainder when $17^{2046}$ is divided by 23?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
22
|
math
|
numina_synthetic_math
|
{
"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": "Consider the parallelepiped $PQRS TUVW$ generated by vectors $\\overrightarrow{PQ},$ $\\overrightarrow{PR},$ and $\\overrightarrow{PT}$. Let $\\overrightarrow{PQ} = 2\\mathbf{i} + \\mathbf{j}$, $\\overrightarrow{PR} = \\mathbf{i} + 2\\mathbf{j} + \\mathbf{k}$, and $\\overrightarrow{PT} = 3\\mathbf{k}$. Calculate the value of:\n\\[\n\\frac{QT^2 + RV^2 + PS^2 + UW^2}{PQ^2 + PR^2 + PT^2}.\n\\]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
3.55
|
math
|
numina_synthetic_math
|
{
"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": "Evaluate $2010^3 - 2009\\cdot 2010^2 - 2009^2\\cdot 2010 + 2009^3.$\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
4019
|
math
|
numina_synthetic_math
|
{
"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": "Determine the value of $b$ such that the lines described by\n\\[\\begin{pmatrix} 3 \\\\ 0 \\\\ -1 \\end{pmatrix} + t \\begin{pmatrix} 1 \\\\ b \\\\ 3 \\end{pmatrix}\\]and\n\\[\\begin{pmatrix} 2 \\\\ -1 \\\\ 4 \\end{pmatrix} + u \\begin{pmatrix} -2 \\\\ 5 \\\\ 1 \\end{pmatrix}\\]are perpendicular.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
-\frac{1}{5}
|
math
|
numina_synthetic_math
|
{
"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 two positive integers is 60, and their difference is 14. What is the value of the positive difference of the squares of these integers?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
840
|
math
|
numina_synthetic_math
|
{
"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 point $(x,y) = (\\cos^2 t, \\sin t \\cos t)$ is plotted for real numbers $t$. Find the type of curve on which all the plotted points lie.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
y^2 = x - x^2
|
math
|
numina_synthetic_math
|
{
"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 $\\frac{1}{8}$ of $2^{36}$ is $8^x$, then what is the value of $x$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
11
|
math
|
numina_synthetic_math
|
{
"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 puppy, a smaller cat, and a larger cat together weigh 30 pounds. The puppy and the larger cat together weigh three times as much as the smaller cat, and the puppy together with the smaller cat weighs five pounds less than the larger cat. Determine the weight of the puppy.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
5
|
math
|
numina_synthetic_math
|
{
"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 quadratic function $y=3x^2 - 12x + 800$, find the minimum value of $y$ under the condition that $x$ is a non-negative integer.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
788
|
math
|
numina_synthetic_math
|
{
"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 positive number is called $n$-primable if it is divisible by $n$ and each of its digits is a one-digit prime number. How many 5-primable positive integers are there that are less than 1000?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
69
|
math
|
numina_synthetic_math
|
{
"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": "What is the 405th digit to the right of the decimal point when $\\frac{18}{47}$ is expressed as a decimal?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
0
|
math
|
numina_synthetic_math
|
{
"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 equation $16 = 4(4)^{x-1}$ for $x$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
x = 2
|
math
|
numina_synthetic_math
|
{
"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 basketball league has twelve teams. During the regular season, each of the twelve teams plays exactly four games against each of the other teams. Additionally, each team must participate in two knockout matches. Calculate the total number of games played during the regular season and knockout matches combined.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
276 \text{ total games}
|
math
|
numina_synthetic_math
|
{
"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 members of a choir are arranged in a rectangular formation. When they are arranged in 10 rows, there are 4 positions unoccupied in the formation. When they are arranged in 11 rows, there are 5 positions unoccupied. How many members are in the choir if the membership is between 200 and 300?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
226
|
math
|
numina_synthetic_math
|
{
"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 \\( y = kx^{\\frac{1}{3}} \\) and \\( y=4 \\) at \\( x=8 \\), what is the value of \\( y \\) when \\( x = 27 \\)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
6
|
math
|
numina_synthetic_math
|
{
"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 $a$ and $b$ be complex numbers, and $r, s, t$ distinct complex roots such that the polynomial $p(z) = (z - r)(z - s)(z - t)$ is transformed under $z \\to az + b$ to $q(z) = (z - cr)(z - cs)(z - ct)$. Find the number of distinct possible values of $c$ under this transformation.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
4
|
math
|
numina_synthetic_math
|
{
"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 a certain positive integer $n,$ there exist real numbers $x_1,$ $x_2,$ $\\dots,$ $x_n$ such that\n\\[\nx_1 + x_2 + x_3 + \\dots + x_n = 1200,\n\\]\n\\[\nx_1^4 + x_2^4 + x_3^4 + \\dots + x_n^4 = 800000.\n\\]\nFind the smallest positive integer $n$ for which this is possible.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
148
|
math
|
numina_synthetic_math
|
{
"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 $f(x)$ be a polynomial of degree 2010 with real coefficients, and let its roots be $r_1,$ $r_2,$ $\\dots,$ $r_{2010}.$ There are exactly 1008 distinct values among\n\\[|r_1|, |r_2|, \\dots, |r_{2010}|.\\] What is the minimum number of real roots that $f(x)$ can have?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
6
|
math
|
numina_synthetic_math
|
{
"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 revised proposal suggests making years that end in double zeroes a leap year only if the year leaves a remainder of 200, 600, 300, or 700 when divided by 1000. How many leap years will there be that end in double zeroes between 2000 and 4000 under this new proposal?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
8
|
math
|
numina_synthetic_math
|
{
"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 $3 \\cdot 7^{-1} + 9 \\cdot 13^{-1} \\pmod{72}$.\n\nExpress your answer as an integer from $0$ to $71$, inclusive.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
18
|
math
|
numina_synthetic_math
|
{
"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 for $x$ and $y$ in the following system of equations:\n1. $\\frac{2x - 3}{3x - y} = \\frac{3}{5}$\n2. $x^2 + y = 7$\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
(-\frac{2}{3}, \frac{47}{9}) \text{ and } (3, 4)
|
math
|
numina_synthetic_math
|
{
"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": "What is the arithmetic mean of all positive three-digit multiples of 6?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
549
|
math
|
numina_synthetic_math
|
{
"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 survey, $82.5\\%$ of respondents believed that mice were dangerous. Of these, $52.4\\%$ incorrectly thought that mice commonly caused electrical fires. Given that these 27 respondents were mistaken, determine the total number of people surveyed.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
63
|
math
|
numina_synthetic_math
|
{
"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 how many integer values of $n$ between 1 and 360 inclusive does the decimal representation of $\\frac{n}{350}$ terminate?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
51
|
math
|
numina_synthetic_math
|
{
"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": "Line segment \\( \\overline{CD} \\) is extended past \\( D \\) to point \\( Q \\) such that \\( CQ:QD = 7:2 \\). Then\n\\[\n\\overrightarrow{Q} = r \\overrightarrow{C} + s \\overrightarrow{D}\n\\]\nfor some constants \\( r \\) and \\( s \\). Enter the ordered pair \\( (r, s) \\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\left( \frac{7}{9}, \frac{2}{9} \right)
|
math
|
numina_synthetic_math
|
{
"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 how many ways can 8 people be seated in a row of chairs if two specific pairs of people, namely Wilma and Paul, and Harry and Sally, refuse to sit next to each other?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
23040
|
math
|
numina_synthetic_math
|
{
"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": "How many different five-letter words can be formed such that they start and end with the same letter, and the middle letter is always 'A'?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
17576
|
math
|
numina_synthetic_math
|
{
"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": "What is the value of $(10! \\cdot 6! \\cdot 3!) / (9! \\cdot 7!)$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{60}{7}
|
math
|
numina_synthetic_math
|
{
"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 largest integer less than 100 that leaves a remainder of 5 when divided by 8.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
93
|
math
|
numina_synthetic_math
|
{
"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": "Determine the value of: $21^2 - 19^2 + 17^2 - 15^2 + 13^2 - 11^2 + 9^2 - 7^2 + 5^2 - 3^2$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
240
|
math
|
numina_synthetic_math
|
{
"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 digits of a four-digit positive integer add up to 18. The sum of the two middle digits is ten, and the thousands digit minus the units digit is two. If the integer is divisible by 9, what is the integer?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
5643
|
math
|
numina_synthetic_math
|
{
"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 lengths of all edges of a rectangular prism are 88 cm. If the height is twice the width and the length is four times the width, find the volume of the prism.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{85184}{343} \text{ cm}^3
|
math
|
numina_synthetic_math
|
{
"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 $QCB$, formed by three tangents to circle $D$, and $\\angle CQB = 60^\\circ$, determine $\\angle COD$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
120^\circ
|
math
|
numina_synthetic_math
|
{
"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": "Place each of the digits 4, 6, 7, and 9 in exactly one square to make the smallest possible product. Afterwards, add 100 to the product. What is the final result? [asy]draw((0,.5)--(10,.5),linewidth(1));\ndraw((4,1)--(6,1)--(6,3)--(4,3)--(4,1),linewidth(1));\ndraw((7,1)--(9,1)--(9,3)--(7,3)--(7,1),linewidth(1));\ndraw((7,4)--(9,4)--(9,6)--(7,6)--(7,4),linewidth(1));\ndraw((4,4)--(6,4)--(6,6)--(4,6)--(4,4),linewidth(1));\ndraw((1,3)--(2,4),linewidth(1));\ndraw((1,4)--(2,3),linewidth(1)); [/asy]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
3343
|
math
|
numina_synthetic_math
|
{
"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 zoo has six pairs of different animals, one male and one female for each. The zookeeper wishes to feed the animals in a specific pattern: each time he feeds a single animal, the next one he feeds must be from a different species and a different gender. If he starts by feeding the male lion, how many ways can he feed all the animals?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
14400
|
math
|
numina_synthetic_math
|
{
"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": "Determine the value of $\\frac{2024^3 - 3 \\cdot 2024^2 \\cdot 2025 + 4 \\cdot 2024 \\cdot 2025^2 - 2025^3 + 2}{2024 \\cdot 2025}$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
2025 - \frac{1}{4089480}
|
math
|
numina_synthetic_math
|
{
"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": "What is the value of $101^3 + 3(101^2)(2) + 3(101)(2^2) + 2^3$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
1,092,727
|
math
|
numina_synthetic_math
|
{
"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 $g$ be a function taking the nonnegative integers to the nonnegative integers, such that\n\\[2g(a^2 + b^2) = [g(a)]^2 + [g(b)]^2\\] for all nonnegative integers $a$ and $b.$\n\nLet $n$ be the number of possible values of $g(16),$ and let $s$ be the sum of the possible values of $g(16).$ Find $n \\times s.$\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
99
|
math
|
numina_synthetic_math
|
{
"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 three numbers $x, y,$ and $z$ is 72. If we decrease $x$ by 9, we get the value $M$. If we increase $y$ by 9, we get the value $M$. If we multiply $z$ by 9, we also get the value $M$. What is the value of $M$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
34
|
math
|
numina_synthetic_math
|
{
"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 $\\cos 150^\\circ$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
-\frac{1}{2}
|
math
|
numina_synthetic_math
|
{
"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 circle has an area of \\( M \\text{ cm}^2 \\) and a circumference of \\( N \\text{ cm} \\). If \\( \\dfrac{M}{N} = 25 \\), what is the radius of the circle, in cm?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
50 \text{ cm}
|
math
|
numina_synthetic_math
|
{
"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": "How many integers $n$ are there such that $4 \\leq n \\leq 15$ and $12321_n$ (the number written as $12321$ in base $n$) is a perfect square?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
12
|
math
|
numina_synthetic_math
|
{
"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": "What is the degree measure of the supplement of the complement of a 30-degree angle?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
120^\circ
|
math
|
numina_synthetic_math
|
{
"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 $\\arctan \\frac{3}{7} + \\arctan \\frac{7}{3}$. Express your answer in radians.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{\pi}{2}
|
math
|
numina_synthetic_math
|
{
"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 number of distinct numbers in the list\n\\[\n\\left\\lfloor \\frac{1^2}{500} \\right\\rfloor, \\ \\left\\lfloor \\frac{2^2}{500} \\right\\rfloor, \\ \\left\\lfloor \\frac{3^2}{500} \\right\\rfloor, \\ \\dots, \\ \\left\\lfloor \\frac{2000^2}{500} \\right\\rfloor.\n\\]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
8000
|
math
|
numina_synthetic_math
|
{
"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": "Determine the complex number $z$ that satisfies the equation $3z + 4i\\bar{z} = -1 - 6i$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{31 + 42i}{75}
|
math
|
numina_synthetic_math
|
{
"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 \\(7(4 - 2i) + 5i(7 - 2i)\\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
38 + 21i
|
math
|
numina_synthetic_math
|
{
"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 $g(x) = 3x^2 - x + 4$. What is the value of $g(g(3))$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
2328
|
math
|
numina_synthetic_math
|
{
"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 \\( a \\) and \\( b \\) be real numbers. Find the maximum value of \\( a e^{\\theta} + b e^{-\\theta} \\) where \\( \\theta \\) is a real number.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
2\sqrt{ab}
|
math
|
numina_synthetic_math
|
{
"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": "Rodney is thinking of a different secret number based on these criteria:\n\\begin{tabular}{ c }\nIt is a two-digit integer.\\\\\nThe tens digit is even.\\\\\nThe units digit is odd.\\\\\nThe number is greater than 75.\n\\end{tabular}\nIf Rodney guesses a number that fits all these conditions, what is the probability that he guesses the correct number? Express your answer as a common fraction.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{1}{10}
|
math
|
numina_synthetic_math
|
{
"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": "What is the smallest integer value of $x$ for which $7 - 3x < 22$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
-4
|
math
|
numina_synthetic_math
|
{
"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 how many distinct five-digit positive integers exist such that the product of their digits equals 18.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
60
|
math
|
numina_synthetic_math
|
{
"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 \\(\\sum_{n = 0}^{\\infty}\\cos^{2n}\\theta = 10\\), what is the value of \\(\\cos{2\\theta}\\)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{4}{5}
|
math
|
numina_synthetic_math
|
{
"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 each pair of real numbers $x \\neq y$, define the operation $\\diamond$ as \\[\n(x \\diamond y) = \\frac{x^2 + y^2}{x - y}.\n\\]What is the value of $((3 \\diamond 1) \\diamond 2)$?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
\frac{29}{3}
|
math
|
numina_synthetic_math
|
{
"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": "What is the midpoint of the segment with endpoints \\((5, -3)\\) and \\((-7, 9)\\)?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
(-1, 3)
|
math
|
numina_synthetic_math
|
{
"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\n\\[\\mathbf{B} = \\begin{pmatrix} 2 & 4 \\\\ 3 & 2 \\end{pmatrix},\\] then compute \\(\\det (\\mathbf{B}^2 - 3 \\mathbf{B}).\\)\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
88
|
math
|
numina_synthetic_math
|
{
"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 the expression \\( i^0 + i^1 + \\cdots + i^{2012} \\).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
1
|
math
|
numina_synthetic_math
|
{
"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\n\\[\\sec x \\tan y + \\sec y \\tan x = 4 \\quad \\text{and} \\quad \\csc x \\cot y + \\csc y \\cot x = 2,\\]\nthen find $\\frac{\\tan x}{\\tan y} + \\frac{\\tan y}{\\tan x}.$\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
8
|
math
|
numina_synthetic_math
|
{
"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": "Evaluate the product \\[ (n-2) \\cdot (n-1) \\cdot n \\cdot (n+1) \\cdot (n+2) \\cdot (n+3), \\] where $n=3$.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
],
"role": "user"
}
] |
720
|
math
|
numina_synthetic_math
|
{
"index": 0,
"split": "dummy"
}
|
train
|
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