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Preflop: I agree with the check. A4s suited isn’t strong enough to raise and plays well enough multi-way. In a loose game a raise is likely to just bloat the pot without thinning the field much.
Flop: I prefer a call over a raise. With the nut flush draw, I don’t mind keep other players in. This keeps the pot smaller and gives you a lower price to call on future streets. With call by you, HJ, and CO, the pot is 2.8. Turn bet of 2/3 pot would then be 1.85. Being in position to the SB, you always that the option to raise if you hit your flush.
Turn: This is close between a call and a jam. You have enough implied odds to call and try to hit your flush. By jamming you can possibly get HJ to fold out their equity and SB to call with a worse draw.
River: This really depends on your read of SB. Would they triple barrel with a draw?
Fold seems reasonable.