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"<|im_start|>system\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end(...TRUNCATED) | ["To solve this problem, we need to find the maximum value of $n$ for which the sum of the first $n$(...TRUNCATED) | 1008 | [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0,0.0,0.0,1.0(...TRUNCATED) |
"<|im_start|>system\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end(...TRUNCATED) | ["In $\\triangle ABC$, the angles $A$, $B$, $C$ form a geometric progression, so let's assume the an(...TRUNCATED) | \frac{2\pi}{7} | [0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,1.0(...TRUNCATED) |
"<|im_start|>system\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end(...TRUNCATED) | ["We need to find the intersection point \\( P(x, y) \\) of the two lines \\( x + my - 2 = 0 \\) and(...TRUNCATED) | 10 | [0.0,0.0,0.0,1.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) |
"<|im_start|>system\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end(...TRUNCATED) | ["To find the matrix that corresponds to reflecting over the vector $\\begin{pmatrix} 4 \\\\ 1 \\end(...TRUNCATED) | \begin{pmatrix} 15/17 & 8/17 \\ 8/17 & -15/17 \end{pmatrix} | [1.0,0.0,1.0,1.0,1.0,0.0,0.0,1.0,1.0,1.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0,1.0,1.0,0.0(...TRUNCATED) |
"<|im_start|>system\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end(...TRUNCATED) | ["The given equation of the circle is in the form $(x-h)^2 + (y-k)^2 = r^2$, where $(h, k)$ is the c(...TRUNCATED) | (3,0) | [1.0,1.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) |
"<|im_start|>system\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end(...TRUNCATED) | ["To find the mean value of the measures of the four interior angles of any quadrilateral, we need t(...TRUNCATED) | 90^\circ | [1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) |
"<|im_start|>system\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end(...TRUNCATED) | ["To determine the number of $3$-inch by $4$-inch rectangles that can be cut from a $24$-inch by $20(...TRUNCATED) | 40 | [1.0,1.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,0.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0,1.0(...TRUNCATED) |
"<|im_start|>system\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end(...TRUNCATED) | ["To determine the value of \\(a\\) that makes the lines \\(l_1\\) and \\(l_2\\) perpendicular, we n(...TRUNCATED) | 0 \text{ or } 1 | [0.0,0.0,0.0,1.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0(...TRUNCATED) |
"<|im_start|>system\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end(...TRUNCATED) | ["The problem describes a uniformly accelerated motion with a constant deceleration of 10 feet/s^2, (...TRUNCATED) | 5 | [0.0,0.0,0.0,0.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0(...TRUNCATED) |
"<|im_start|>system\nPlease reason step by step, and put your final answer within \\boxed{}.<|im_end(...TRUNCATED) | ["Xiaoqiang made a mistake when subtracting an algebraic expression $-3ab+5bc-1$ due to carelessness(...TRUNCATED) | 7ab - 13bc + 8 | [0.0,1.0,1.0,0.0,1.0,0.0,0.0,1.0,0.0,0.0,0.0,0.0,1.0,1.0,0.0,1.0,0.0,0.0,0.0,0.0,0.0,0.0,1.0,1.0,0.0(...TRUNCATED) |
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