Propose Subgoal Decomposition Plans

Use this skill when the agent has enough context to propose several viable decomposition plans.

Input Contract

Read:

• the current target theorem or branch goal
• relevant immediate_conclusions, toy_examples, and counterexamples
• relevant failed_paths and branch_states
• recent search results and useful references from events

Procedure

1. Gather the current information that materially constrains the problem: useful examples, failed claims, known obstructions, and relevant search results.
2. Propose materially different decomposition plans.
3. For each plan, state:
   • the main idea of the plan
   • the ordered subgoals
   • why this plan is plausible given the current information
   • which earlier failures or counterexamples it tries to avoid
4. Hand each plan to $direct-proving for a quick screening pass.

Output Contract