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I don't think you are necessarily right to think that you induced a bluff with your min-re-raise. They often represent a lot of strength and imo he is just as likely to have been timing out considering what line he should take with QQ/JJ/AK etc as working out that he could bluff you.

You have to fold now I think.

Re-raising pot (or a bit more) here would be totally standard. Why on earth did you min- it?