{"task": {"agent_timeout": 3000, "task": "aime_ii-5", "verifier_timeout": 3000, "instruction": "  Solve the following problem. Reason step by step, create the file `/app/answer.txt`, and put your final answer there.\n  Your answer should be a single integer from 1 to 999 inclusive.\n\n    Suppose $\\triangle ABC$ has angles $\\angle BAC = 84^\\circ$, $\\angle ABC = 60^\\circ$, and $\\angle ACB = 36^\\circ$. Let $D$, $E$, and $F$ be the midpoints of sides $\\overline{BC}$, $\\overline{AC}$, and $\\overline{AB}$, respectively. The circumcircle of $\\triangle DEF$ intersects $\\overline{BD}$, $\\overline{AE}$, and $\\overline{AF}$ at points $G$, $H$, and $J$, respectively. The points $G$, $D$, $E$, $H$, $J$, and $F$ divide the circumcircle of $\\triangle DEF$ into six minor arcs, as shown. Find $\\wideparen{DE} + 2 \\cdot \\wideparen{HJ} + 3 \\cdot \\wideparen{FG}$, where the arcs are measured in degrees.\n\n  \\begin{tikzpicture}[scale=1.2]\n      \\coordinate (B) at (0,0);\n      \\coordinate (C) at (6,0);\n      \\coordinate (A) at (1.78,3.07);\n\n      \\coordinate (D) at ($(B)!0.5!(C)$);\n      \\coordinate (E) at ($(A)!0.5!(C)$);\n      \\coordinate (F) at ($(A)!0.5!(B)$);\n\n      \\draw (A) -- (B) -- (C) -- cycle;\n\n      \\fill (A) circle (2pt) node[above] {$A$};\n      \\fill (B) circle (2pt) node[below] {$B$};\n      \\fill (C) circle (2pt) node[below] {$C$};\n\n      \\fill (D) circle (2pt) node[below] {$D$};\n      \\fill (E) circle (2pt) node[right] {$E$};\n      \\fill (F) circle (2pt) node[left] {$F$};\n\n      \\draw (D) -- (E) -- (F) -- cycle;\n\n      \\coordinate (O) at (2.39,1.38);\n\n      \\draw (O) circle (1.51);\n\n      \\coordinate (G) at (1.72, 0.03);\n      \\coordinate (J) at (1.5, 2.6);\n      \\coordinate (H) at (2.08, 2.85);\n\n      \\fill (G) circle (2pt) node[below] {$G$};\n      \\fill (H) circle (2pt) node[above] {$H$};\n      \\fill (J) circle (2pt) node[above left] {$J$};\n  \\end{tikzpicture}\n", "memory": "", "runnable": false, "difficulty": "unknown", "language": "", "cpus": "", "instruction_truncated": false, "category": "reasoning", "compose": false, "has_solution": true, "oracle": null, "docker_image": "", "taskset": "aime", "tags": ["math", "AIME"]}, "runs": []}