Give users full control over every prompt cook sends to an agent — without making the default template unwieldy. Six gaps were identified where prompts were hidden in TypeScript source or context was unavailable in templates. This PR closes them.

Changes

1. New context variables — agent, model, projectName, gitBranch, branchIndex, branchCount, resolver added to LoopContext and populated throughout the execution path.

2. Config-level prompt overrides — .cook/config.json gains a prompts section (review, gate, iterate, judge, merge, compare). Priority chain: CLI flag > config.json > hardcoded default.

3. Updated DEFAULT_COOK_MD — cook init now generates a template that documents all available variables in a collapsible <details> block. Active template stays under 20 lines.

Key files

Test plan

• npm run build passes
• cook init in a fresh dir produces correct defaults with all variables documented
• cook doctor still works
• A simple cook "test" review run completes (no regressions)
• cook "test" v2 pick "criteria" with custom prompts.judge in config uses the override
• Existing COOK.md files without new variables continue to work unchanged

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