AJs, 3 bet pot vs shorty. Flop plan?

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Bet $26-30ish. It'll look like your trying to milk him and it lets you get away if he's calling/pushing. This flop either hit him hard or totally whiffed him unless he does something stupid like push 77 w/ a spade. Give it one shot and be done w/ it.
I don't like checking for the same reason that a small pp w/ a spade may push if u show weakness, but may fold if u bet. I just check if I think he'll only bet a better hand. Faaak, I dunno. This is a really ghey spot.

This is actually close between betting and just c/folding. What range is this guy calling 3bet w/ and will he stack w/ any piece/spade???

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I initially thought about betting, but I don't like this line because it kinda sounds like we're betting to make sure he doesn't bluff us out of the pot, which doesn't sound like very good logic.