If you're going to check the flop I think you've basically already given up on the hand. Not saying that's necessarily a bad thing. If this is a loose/passive table and it somehow checks all the way around there are so many scare cards on the turn that you can just muck instead of check at that point.
If you check, outside of an EP villain making a 1/3 or 1/2 size bet with a short stack and it folds around to you, what else are you looking for to be comfortable to go forward with? If the flop bettor is a maniac in LP with 200BBs, are you really going to attack back or c/c the rest of the way after a decently coordinated flop with 6 people calling a $38 PFR?
If you choose to lay over and die, that's cool. Not even arguing that you shouldn't. If that's not your choice though, I think you have to place a pretty decent sized bet on the flop, at least $150-200, and hope that's enough to take it down.
Otherwise, just move on to the next hand imo. I don't think check/3b AA into a 7-way flop of JT6ss is going to get you too far in the long run. So many combos you're getting crushed by here (a few you're flipping with and have enough equity, but still...): JJ, TT, 66, K
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