"""Create reasoning_engine
Generated by Phi-Octopus Eden
2025-11-08 08:53:00.042737
"""

```python
from typing import List, Dict

class ReasoningEngine:
    """
    A simple reasoning engine that solves a specific problem of limited reasoning sophistication.
    This implementation focuses on determining if a given list of numbers can be partitioned into two subsets such that the sum of elements in both subsets is equal.

    :param nums: List[int] - The input list of integers
    """

    def __init__(self, nums: List[int]):
        self.nums = nums

    def can_partition(self) -> bool:
        """
        Determines if it's possible to partition the given list into two subsets with equal sum.
        Returns True if such a partition exists, False otherwise.

        :return: bool
        """
        total_sum = sum(self.nums)
        # If total sum is odd, we can't have two subsets with equal sum
        if total_sum % 2 != 0:
            return False

        target_sum = total_sum // 2
        n = len(self.nums)
        dp = [[False for _ in range(target_sum + 1)] for _ in range(n + 1)]

        # Base case: Zero sum is always possible with empty subset
        for i in range(n + 1):
            dp[i][0] = True

        # Fill the partition table in a bottom-up manner
        for i in range(1, n + 1):
            for j in range(1, target_sum + 1):
                if self.nums[i - 1] <= j:
                    dp[i][j] = dp[i - 1][j] or dp[i - 1][j - self.nums[i - 1]]
                else:
                    dp[i][j] = dp[i - 1][j]

        return dp[n][target_sum]


# Example usage
if __name__ == "__main__":
    nums = [1, 5, 11, 5]
    engine = ReasoningEngine(nums)
    result = engine.can_partition()
    print(f"Can partition into two subsets with equal sum: {result}")
```

This Python code defines a `ReasoningEngine` class that attempts to solve the problem of determining whether a given list of integers can be partitioned into two subsets such that the sum of elements in both subsets is equal. The example usage demonstrates how to use this class for a specific input.