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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 devel... | [
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"from": "user",
"value": "## Task B-1.3.\n\nA ship traveling along a river has covered $24 \\mathrm{~km}$ upstream and $28 \\mathrm{~km}$ downstream. For this journey, it took half an hour less than for traveling $30 \\mathrm{~km}$ upstream and $21 \\mathrm{~km}$ downstream, or half an hour more than for ... |
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 devel... | [
{
"from": "user",
"value": "3. (6 points) A construction company was building a tunnel. When $\\frac{1}{3}$ of the tunnel was completed at the original speed, they started using new equipment, which increased the construction speed by $20 \\%$ and reduced the working hours to $80 \\%$ of the original. As a ... |
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 devel... | [
{
"from": "user",
"value": "Prove that number $1$ can be represented as a sum of a finite number $n$ of real numbers, less than $1,$ not necessarily distinct, which contain in their decimal representation only the digits $0$ and/or $7.$ Which is the least possible number $n$?"
},
{
"from": "assista... |
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 devel... | [
{
"from": "user",
"value": "4. Given the three sides of an obtuse triangle are 3, $4, x$, then the range of values for $x$ is ( ).\n(A) $1<x<7$.\n(B) $5 \\ll x<7$.\n(C) $1<x<\\sqrt{7}$.\n(D) $5<x<7$ or $1<x<\\sqrt{7}$."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\nOkay, so I have th... |
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 devel... | [
{
"from": "user",
"value": "1. Solve the equation: $\\frac{8 x+13}{3}=\\frac{19-12 x}{2}-\\left(16 x-\\frac{7-4 x}{6}\\right)$."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\nOkay, so I need to solve this equation: (8x + 13)/3 = (19 - 12x)/2 - (16x - (7 - 4x)/6). Hmm, that looks a bi... |
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 devel... | [
{
"from": "user",
"value": "A right-angled triangle has side lengths that are integers. What could be the last digit of the area's measure, if the length of the hypotenuse is not divisible by 5?"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\nOkay, so I need to figure out the possible... |
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 devel... | [
{
"from": "user",
"value": "Let $a_n\\ (n\\geq 1)$ be the value for which $\\int_x^{2x} e^{-t^n}dt\\ (x\\geq 0)$ is maximal. Find $\\lim_{n\\to\\infty} \\ln a_n.$"
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\nOkay, so I need to find the limit as n approaches infinity of the natural ... |
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 devel... | [
{
"from": "user",
"value": "11. Given that the internal angles $A, B, C$ of $\\triangle ABC$ have opposite sides $a, b, c$ respectively, and $\\sqrt{3} b \\cos \\frac{A+B}{2}=c \\sin B$.\n(1) Find the size of $\\angle C$;\n(2) If $a+b=\\sqrt{3} c$, find $\\sin A$."
},
{
"from": "assistant",
"val... |
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 devel... | [
{
"from": "user",
"value": "Task B-4.2. Let $n$ be the number obtained by writing 2013 zeros between every two digits of the number 14641. Determine all solutions of the equation $x^{4}=n$ in the set $\\mathbb{C}$."
},
{
"from": "assistant",
"value": "<|begin_of_thought|>\nOkay, so I need to sol... |
"\n\nYour role as an assistant involves thoroughly exploring questions through a systematic long thi(...TRUNCATED) | [{"from":"user","value":"6. As shown in Figure 2, let $P$ be a point inside the equilateral $\\trian(...TRUNCATED) |
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