"""Create reasoning_engine
Generated by Phi-Octopus Eden
2025-11-08 14:00:05.647899
"""

```python
from typing import List, Dict, Any

class ReasoningEngine:
    """
    A basic reasoning engine that can solve simple logical problems.
    This implementation focuses on solving a common constraint satisfaction problem: 
    finding valid assignments for variables under given constraints.

    Args:
        variables (List[str]): The names of the variables to be assigned values.
        domains (Dict[str, List[Any]]): A dictionary mapping each variable to its possible values.
    
    Attributes:
        solutions (List[Dict[str, Any]]): A list containing all valid assignments as dictionaries.
    """

    def __init__(self, variables: List[str], domains: Dict[str, List[Any]]):
        self.variables = variables
        self.domains = domains
        self.solutions = []

    def is_consistent(self, assignment: Dict[str, Any], variable: str) -> bool:
        """
        Check if the current assignment is consistent with the constraints.

        Args:
            assignment (Dict[str, Any]): The current partial assignment.
            variable (str): The variable being assigned a value.

        Returns:
            bool: True if the current state of the variables satisfies all constraints,
                  otherwise False.
        """
        return True  # Placeholder implementation

    def backtracking_search(self) -> None:
        """
        Perform a backtracking search to find all valid assignments for the given problem.
        """
        self._search({}, 0)

    def _search(self, assignment: Dict[str, Any], var_index: int) -> None:
        if var_index == len(self.variables):
            # All variables are assigned
            self.solutions.append(assignment.copy())
            return

        variable = self.variables[var_index]
        for value in self.domains[variable]:
            new_assignment = assignment.copy()
            new_assignment[variable] = value
            if self.is_consistent(new_assignment, variable):
                self._search(new_assignment, var_index + 1)

    def get_solutions(self) -> List[Dict[str, Any]]:
        """
        Return all the valid assignments found.

        Returns:
            List[Dict[str, Any]]: A list of dictionaries where each dictionary represents a solution.
        """
        return self.solutions

# Example usage
if __name__ == "__main__":
    # Define the problem constraints
    variables = ['x', 'y']
    domains = {'x': [1, 2], 'y': [3, 4]}

    # Create and run the reasoning engine
    engine = ReasoningEngine(variables, domains)
    engine.backtracking_search()

    print("Solutions:", engine.get_solutions())
```