- Add new prompts database table for system prompt management
- Create admin prompts page with analyze and training sections
- Add prompts management UI with separate areas for different functionalities
- Update analyze page with audio analysis and video splitting checkboxes
- Modify analyze API to handle new prompt composition logic
- Update worker_analyze to handle multi-step prompts (video + audio)
- Fix stats reload blinking in analyze page right panel by updating only changing sections
- Add prompts link to admin menu navigation

All changes follow the AI.PROMPT rules for database migrations and API updates.