idx int64 0 5.62k | prompt stringlengths 754 12.8k | answers sequencelengths 8 8 | gt stringlengths 1 839 | true_reward bool 2
classes |
|---|---|---|---|---|
1,001 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
In the conve... | [
"To solve this problem accurately, we need to reconsider the conditions and properties of the quadrilateral. Given that \\(AD = DC = CB = x\\) and \\(AC = BD = AB = y\\), the quadrilateral \\(ABCD\\) is cyclic and symmetric. We can use the properties of cyclic quadrilaterals and symmetry to find the ratio \\(\\frac... | \frac{\sqrt{5}-1}{2} | true |
3,348 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
For how many... | [
"Let's correct the solution by re-evaluating the problem without gerrymandering the interval \\([0, 2000]\\) in incorrect parts. Our goal here is to count all numbers of the type \\(8n\\), \\(8n+3\\), and \\(8n+6\\) that lie within the interval.\n\nAfter re-evaluation:\n\n1. Natural \\(n\\) and consideration must e... | 501 | false |
3,101 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Given the ex... | [
"Since we have previously confirmed that the expression \\(\\frac{a^2}{b} + \\frac{ab}{a^2 - b} - \\frac{b^2}{a - b} - \\frac{b}{a}\\) is already in its simplest form, I conclude that there are no further simplifications possible. There is no",
"The initial response appears to be correct, given the problem's cons... | \frac{a^2+ab+b^2}{b} | false |
2,064 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Let $n$ be t... | [
"I apologize for the initial incorrect solution. Let's carefully analyze the problem again and ensure we correctly identify the largest integer $n$ that is the product of exactly 3 distinct prime numbers $d$, $e$, and $d^2 + 10e$, where $d$ and $e$ are single-digit primes.\n\nWe'll again start by listing the single... | 9 | false |
2,847 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Suppose that... | [
"Let's review the earlier steps to ensure everything is accurate. Given $5 = b + b^{-1}$, we proceed as follows:\n\n1. Let $x = b + b^{-1} = 5$.\n2. Calculate $b^2 + b^{-2}$ using the identity: \n \\[\n b^2 + b^{-2} = (b + b^{-1})^2 - 2 = x^2 - 2 = 5^2 - 2 = 25 - 2 = 23\n \\]\n3. Calculate $b^4 + b^{-4}$ usin... | 12119 | false |
2,196 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Given the fu... | [
"Let's break down the problem again step by step and output the final answer within \\boxed{}.\n\n### Part (1): When $a=0$, find the maximum value of $f(x)$\n\n1. **Substitute $a=0$ into the function $f(x)$:**\n \\[\n f(x) = -\\frac{1}{x} - \\ln x\n \\]\n\n2. **Find the derivative of $f(x)$:**\n \\[\n f'(... | (0,+\infty) | false |
5,142 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
**p1.** Will... | [
"Let's fix the issues and provide the correct solutions with the appropriate format.\n\n1. **Problem 1:**\n What is the total area of the surface of a right circular cone of height \\(12\\) and base circle of radius \\(5\\)?\n - The formula for the total surface area \\(A\\) of a cone is given by:\n \\[\n ... | 140 | false |
5,127 | <|im_start|>system
You are a mathematical reasoning assistant. For each problem, follow these steps strictly:
1. Solve the problem using step-by-step reasoning and output the final answer within \boxed{}.
Always ensure clarity, correctness, and adherence to the required format.<|im_end|>
<|im_start|>user
Given the fu... | [
"Let's reason step by step again. The problem asks us to find the range of \\(a\\) such that there exist two distinct points on the graph of the piecewise function \\( f(x) = \\begin{cases} x^2 + x + a, & x < 0 \\\\ -\\frac{1}{x}, & x > 0 \\end{cases} \\) where the tangents coincide.\n\n1. **Find the derivatives:**... | a \in (-2, \frac{1}{4}) | false |
2,514 | "<|im_start|>system\nYou are a mathematical reasoning assistant. For each problem, follow these step(...TRUNCATED) | ["Let's solve the problem step by step again.\n\nGiven the function \\( y = a \\sin x + b \\) with \(...TRUNCATED) | 1 | false |
4,596 | "<|im_start|>system\nYou are a mathematical reasoning assistant. For each problem, follow these step(...TRUNCATED) | ["Let me re-evaluate the problem and solve it step by step once again to ensure no errors were made (...TRUNCATED) | \rho\sin \left(\theta+ \dfrac{\pi}{4}\right)= \dfrac{ \sqrt{2}}{2} | false |
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