Implement a Thread-Safe Fixed-Size Thread Pool

Implement a FixedSizeThreadPool class in C++. This thread pool should be able to execute submitted tasks asynchronously. The pool should have a fixed number of worker threads that are created upon initialization and persist for the lifetime of the pool. When the FixedSizeThreadPool is destroyed, all pending tasks should be completed, and worker threads should be gracefully shut down.

Your implementation must correctly handle:

1. Task Submission: A method to add new tasks (callable objects) to a queue.
2. Worker Thread Management: Threads should pick up tasks from the queue and execute them.
3. Synchronization: Ensure thread safety for task queue access and proper signaling between task submission and task execution, preventing race conditions or deadlocks.
4. Graceful Shutdown: All submitted tasks must be processed before the pool's destructor completes, and worker threads must terminate cleanly.

The provided starter code has a basic structure but is missing critical synchronization mechanisms and graceful shutdown logic, leading to potential race conditions, busy-waiting, deadlocks, or improper resource management.