{"task": {"agent_timeout": 600, "task": "omnimath_1042", "verifier_timeout": 60, "instruction": "# Mathematical Problem\n\nLet $A B C$ be a triangle with $A B=13, A C=14$, and $B C=15$. Let $G$ be the point on $A C$ such that the reflection of $B G$ over the angle bisector of $\\angle B$ passes through the midpoint of $A C$. Let $Y$ be the midpoint of $G C$ and $X$ be a point on segment $A G$ such that $\\frac{A X}{X G}=3$. Construct $F$ and $H$ on $A B$ and $B C$, respectively, such that $F X\\|B G\\| H Y$. If $A H$ and $C F$ concur at $Z$ and $W$ is on $A C$ such that $W Z \\| B G$, find $W Z$.\n\n## Instructions\n\nSolve the mathematical problem above and write your final answer to `/workspace/answer.txt`.\n\n**Important**: Write only your final answer to the file, not the full solution process.\n\n### Guidelines\n\n- Provide your final numerical answer or mathematical expression\n- Write the answer as plain text (no special formatting needed)\n- Be precise and clear in your answer\n- The answer should directly respond to what the problem asks for\n\n### Example\n\nIf the problem asks \"What is 2 + 2?\", your answer file should contain:\n\n```\n4\n```\n\nYour answer will be evaluated against the correct solution using an automated grading system.\n", "memory": "", "runnable": false, "difficulty": "hard", "language": "", "cpus": "", "instruction_truncated": false, "category": "math", "compose": false, "has_solution": true, "oracle": null, "docker_image": "", "taskset": "omnimath", "tags": ["omni-math"]}, "runs": []}