Rust Error Handler And Logger

**Context**: 
Design a robust error handler and logger for a Rust application, focusing on providing informative error messages, categorizing errors, and logging mechanisms for debugging and monitoring purposes. The error handler should be capable of handling various types of errors, including runtime errors, syntax errors, and custom application-specific errors.

**Detailed Instructions**:
1. Develop a custom error type that can encapsulate different error variants, including but not limited to, `IOError`, `NetworkError`, `DatabaseError`, and `UnknownError`. Each variant should have associated details such as error message and optional additional context (e.g., file path for `IOError`, URL for `NetworkError`).
2. Implement a logger that can log errors at different levels (e.g., debug, info, warn, error, fatal). The logger should be configurable to log to the console, file, or both, with the ability to customize log format and verbosity level.
3. Create a global error handler function that catches and processes all unhandled errors, logs them using the custom logger, and then performs appropriate actions based on the error type (e.g., exit the application for fatal errors, retry for transient errors).
4. Integrate the error handler with the logger to ensure all errors are logged appropriately, including the error message, error type, and any additional context.
5. Ensure the solution is extensible, allowing for easy addition of new error types and custom error handling logic without modifying the existing codebase.

**Output Format**:
The solution should be presented as a Rust code snippet that includes:
- The definition of the custom error type.
- The implementation of the logger.
- The global error handler function.
- Example usage demonstrating how to use the custom error type, logger, and error handler in a Rust application.

**Examples**:
- An example of logging an `IOError` when attempting to read from a non-existent file.
- An example of handling a `NetworkError` by retrying the network request.
- An example of customizing the logger to log errors to both console and file with a specific format.