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It's an extract from a conversation (the task was to complete the gaps with the auxiliary verbs).

A: So you do go out much then?

B: Well, I do go out but I don't go to clubs very often.

A: Oh, I do. I love clubbing.

Did I do it correctly? If yes, what are the meanings of the first two "do"?

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A: So you don't go out much then?
B: Well, I do go out but I don't go to clubs very often.
A: Oh, I do. I love clubbing.

In the first sentence, "don't" is used to form a negative statement in the normal way. (The sentence is framed as a question, but grammatically it is actually a statement.)

"do" in the second sentence is used for emphasis. This use is common when contradicting something that someone else has said or implied.