Calculate the XOR of all pile sizes. If the result is zero, the first player cannot force a win (return `false`). Otherwise, proceed to the next hint.

If the XOR is non-zero, the first player can force a win by making a move that reduces one pile such that the new XOR of all piles becomes zero. Identify which pile(s) can be modified to achieve this.

For the identified pile(s), determine the exact number of stones to remove (e.g., `piles[i] ^ total_xor`) to make the new XOR zero. If such a move exists, the first player can force a win (return `true`); otherwise, return `false`.