"""Create recovery_planner
Generated by Phi-Octopus Eden
2025-11-07 10:53:20.219176
"""

```python
from typing import List, Dict

class RecoveryPlanner:
    """
    A class for creating a limited error recovery planner.
    
    Methods:
        plan_recovery: Plans a recovery action based on an error state.
    """

    def __init__(self, max_errors: int = 5):
        self.max_errors = max_errors
        self.error_count: Dict[str, int] = {}

    def plan_recovery(self, error_state: str) -> bool:
        """
        Plan a recovery action for the given error state if within limits.
        
        Args:
            error_state (str): The current error state.
            
        Returns:
            bool: True if a recovery is planned and possible, False otherwise.
        """
        self.error_count[error_state] = self.error_count.get(error_state, 0) + 1
        
        # Check if we have exceeded the max errors for this state
        if self.error_count[error_state] > self.max_errors:
            return False
        
        print(f"Recovery plan initiated for error state: {error_state}")
        
        # Simulate a recovery action
        if error_state == "ConnectionError":
            simulate_recovery_action("Connecting to backup server")
        elif error_state == "TimeoutError":
            simulate_recovery_action("Retrying request in 5 seconds")
        
        return True

def simulate_recovery_action(action: str):
    """
    Simulates an action taken during recovery.
    
    Args:
        action (str): The action being simulated.
    """
    print(f"Action taken: {action}")

# Example usage
if __name__ == "__main__":
    planner = RecoveryPlanner(max_errors=3)
    
    # Simulate some errors and their recoveries
    for _ in range(5):
        if not planner.plan_recovery("ConnectionError"):
            break
    
    for _ in range(4):
        if not planner.plan_recovery("TimeoutError"):
            break

```

This Python code defines a `RecoveryPlanner` class that plans recovery actions based on an error state, ensuring it does not exceed a set limit of errors. The example usage demonstrates simulating multiple errors and their recoveries within the constraints of the defined limits.