Build an AI time blocking and focus calendar web app with these features:

1. Google Calendar and Outlook integration via OAuth. Import existing events, meetings, and commitments as fixed blocks.

2. Task inbox where users add tasks with priority (high, medium, low), estimated duration, deadline, and energy requirement (deep focus, light work, creative). Tasks can be categorized by project.

3. AI auto-scheduler that takes fixed calendar events plus the task inbox and generates an optimal time-blocked day. Considers: energy patterns (user sets when they are most productive), task priority, deadlines, buffer time between blocks, and lunch and break recommendations.

4. Drag-and-drop calendar view where users can adjust the AI's suggested schedule. Changes auto-rebalance remaining blocks. Color coding by category (deep work, meetings, admin, breaks).

5. Focus mode that starts a timer for the current block, hides notifications, and shows only the current task. Includes optional ambient sound player and a simple note field for capturing thoughts during focus sessions.

6. Energy pattern profiler: user completes a short setup quiz about when they feel most energetic, creative, and focused. AI uses this to schedule deep work during peak hours and lighter tasks during low energy periods.

7. Daily review and planning ritual: each morning, AI presents the day's plan for approval. Each evening, AI asks what got done, what slipped, and adjusts future scheduling based on actual completion patterns.

8. Analytics dashboard showing time spent by category, focus session completion rate, schedule adherence (planned vs actual), and productivity trends over weeks.

9. Recurring block templates: morning routine, deep work morning, meeting afternoon, etc. Users can save and apply templates to speed up planning.

10. Slack and email integration to automatically block time for processing messages during designated admin windows rather than constant context switching.