The idea is to reverse the second half of the linked list and utilize the twin's definition by simultaneously traversing the first half from the beginning and the reversed half from the end. As you do this traversal, calculate the twin sums and keep track of the maximum.

Steps:

1. Find the midpoint of the linked list using a slow and fast pointer approach.
2. Reverse the second half of the linked list.
3. Initialize pointers to traverse the first half and the reversed second half simultaneously.
4. Calculate twin sums and update the maximum twin sum.

This approach makes use of an auxiliary array where we store the values of the linked list nodes. Once stored, we can leverage the structure of the list to easily compute twin sums using simple array indexing.

Steps:

1. Traverse the linked list to populate an array with node values.
2. Using a loop, calculate twin sums by adding corresponding elements from the start and end of the array.
3. Track the maximum sum obtained.