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Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
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"value": "Return your final response within \\boxed{}. Given \\(a_{1}, a_{2}, \\cdots, a_{n}(n \\geqslant 2)\\) are \\(n\\) distinct real numbers, let \\(S = a_{1}^{2} + a_{2}^{2} + \\cdots + a_{n}^{2}\\) and \\(M = \\min_{1 \\leq i < j \\leq n} (a_{i} - a_{j})^{2}\\). Prove that \\(\\frac... | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.ATMs of a well-known bank of a small country are arranged so that they can not give any amount of mo... | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
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"value": "Return your final response within \\boxed{}. To number the pages in a mathematics textbook, 390 digits were required. How many pages are in the mathematics textbook?"
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"value": "<|begin_of_thought|>\n\nOkay, let's see. The problem is asking ho... | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Given that \\( f(x) \\) is an odd function defined on \\( (-\\infty, 0) \\cup (0, +\\infty) \\) and that for \\( x > 0 \\), \\( x f'(x) < 0 \\) and \\( f(1) = 0 \\), determine the solution set of the inequality \\( x f(x) < 0 \\)."
}... | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Generate an executable Python function generated from the given prompt. The function should take stdin as input and print the output. Simply call the function after the definition.You are given a sequence of numbers *a*1,<=*a*2,<=...,<=*a**n*, and a number *m*.\n\nCheck if it is ... | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. Let $p(x) = x^{2008} + x^{2007} + x^{2006} + \\cdots + x + 1,$\nand let $r(x)$ be the polynomial remainder when $p(x)$ is divided by $x^4+x^3+2x^2+x+1$. Find the remainder when $|r(2008)|$ is divided by $1000$.\n"
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{
"from": ... | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
Your role as an assistant involves thoroughly exploring questions through a systematic long thinking process before providing the final precise and accurate solutions. This requires engaging in a comprehensive cycle of analysis, summarizing, exploration, reassessment, reflection, backtracing, and iteration to develop w... | [
{
"from": "user",
"value": "Return your final response within \\boxed{}. $31 \\cdot 36$ satisfies $0 \\leq x \\leq y$ and $\\sqrt{1992}=\\sqrt{x}+\\sqrt{y}$. What is the number of different integer pairs $(x, y)$?\n(A) 0\n(B) 1\n(C) 2\n(D) 4"
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"value": "<|begin_of_though... | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
"Your role as an assistant involves thoroughly exploring questions through a systematic long thinkin(...TRUNCATED) | [{"from":"user","value":"Return your final response within \\boxed{}. From the center \\(O\\) of a r(...TRUNCATED) | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
"Your role as an assistant involves thoroughly exploring questions through a systematic long thinkin(...TRUNCATED) | [{"from":"user","value":"Return your final response within \\boxed{}. Lemma 11.4.1 (Chebyshev's Ineq(...TRUNCATED) | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
"Your role as an assistant involves thoroughly exploring questions through a systematic long thinkin(...TRUNCATED) | [{"from":"user","value":"Generate an executable Python function generated from the given prompt. The(...TRUNCATED) | null | null | null | null | null | null | null | null | null | null | null | null | null | null |
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