- Add InboxTask typing and TaskStore.selectNextTaskForAgent() with priority ordering, dependency checks, paused filtering, and FIFO selection
- Wire heartbeat execution to auto-select and assign inbox work when no task is set, with optional checkout attempts and graceful conflict fallback
- Add POST /api/agents/:id/inbox to expose next-task selection details (task, priority, reason) and return task:null when no work is available
- Expand core, engine, and dashboard tests to cover selection priorities, heartbeat precedence/metadata, checkout-conflict handling, and route behavior with type-safe mocks
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