### What problem does this PR solve?

This commit refactors the core prompts to decouple the high-level
reasoning from the low-level information extraction. By making
REASON_PROMPT a dedicated strategist that only generates search queries
and re-tasking RELEVANT_EXTRACTION_PROMPT to be a specialized tool for
single-fact extraction, we eliminate redundant information
summarization. This clear separation of concerns makes the overall
reasoning process significantly faster and more precise, as each
component now has a single, well-defined responsibility.

### Type of change

- [x] Performance Improvement

### What problem does this PR solve?

#5905

### Type of change

- [x] New Feature (non-breaking change which adds functionality)

### What problem does this PR solve?

#5173

### Type of change

- [x] Refactoring