The correct choice is determined by removing other people from the sentence to identify if 'me' or 'I' is appropriate.
When deciding whether to use me or I, remove other people from the sentence to determine which one is correct. In the sentence Jim asked Tim and me to go fishing, me is correct because you would not say, Jim asked I to go fishing. Conversely, in Tina and I went to the mall, I is correct because you would not say, Me went to the mall.
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