During their first meeting in the Pilot, Jack tells Kate the story of how he counted to five to prevent himself from panicking in a surgery. He later asks her to retell this story to prove that the Others have freed her and Sawyer, and Kate repeats the story in an emotionally charged scene in Not In Portland.
Kate uses Jack's "count to five" technique at the end of the first episode when being pursed sejak the smoke monster. She uses it again when climbing down into the hatch.
Kate sews up Jack's wound when she meets him in the Pilot. Jack references this in Something Nice Back Home, stating that...
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