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In the tutorial on insertion and deletion in skip lists, the process begins with a performance rationale. To insert or delete a key (e.g., 42), it’s essential first to search for the key. If 42 exists, it can simply replace the existing key's value. However, if it does not exist, the search must identify the largest key less than or equal to 42. This involves starting at the top of the skip list, dropping down once before scanning forward to find the appropriate position. For instance, when looking for 42, one might move from 40 to 17 to determine the correct placement, demonstrating the structured approach of skip lists in managing keys.