"""Create reasoning_engine
Generated by Phi-Octopus Eden
2025-11-08 14:54:21.089198
"""

```python
from typing import List


class ReasoningEngine:
    """
    A basic reasoning engine that solves a specific problem of limited reasoning sophistication.
    
    The engine attempts to find the longest common subsequence (LCS) between two sequences,
    which is a problem often encountered in bioinformatics, text comparison, and more.
    """

    def __init__(self):
        pass

    def _lcs_helper(self, s1: str, s2: str, memo: dict = None) -> int:
        """
        Helper function to compute the length of the longest common subsequence (LCS).
        
        :param s1: First sequence as a string
        :param s2: Second sequence as a string
        :param memo: Memoization dictionary to store results of subproblems for efficiency
        :return: Length of LCS between s1 and s2
        """
        if memo is None:
            memo = {}
        
        if (s1, s2) in memo:
            return memo[(s1, s2)]
        
        if not s1 or not s2:
            result = 0
        elif s1[-1] == s2[-1]:
            result = self._lcs_helper(s1[:-1], s2[:-1], memo) + 1
        else:
            result = max(self._lcs_helper(s1, s2[:-1], memo), self._lcs_helper(s1[:-1], s2, memo))
        
        memo[(s1, s2)] = result
        return result

    def find_lcs_length(self, seq1: str, seq2: str) -> int:
        """
        Find the length of the longest common subsequence between two sequences.
        
        :param seq1: First sequence as a string
        :param seq2: Second sequence as a string
        :return: Length of LCS between seq1 and seq2
        """
        return self._lcs_helper(seq1, seq2)


# Example Usage:
if __name__ == "__main__":
    reasoning_engine = ReasoningEngine()
    
    # Example sequences for testing the longest common subsequence function.
    sequence_1 = "AGGTAB"
    sequence_2 = "GXTXAYB"
    
    lcs_length = reasoning_engine.find_lcs_length(sequence_1, sequence_2)
    print(f"The length of the longest common subsequence is: {lcs_length}")
```