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What am I doing wrong?

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Two times yesterday I saw redfish, managed to get the fly in front of them, watched them race over to the fly (although, I can't be 100% sure on this, since I could not actually see my fly), then they get to the spot and stop. It certainly looked like they ate the fly, but I didn't feel anything so I don't set the hook until I can't stand it which point I strip and the fish bolt out of there. I think next time I see this, I'm going to set immediately when they stop like that. What do you guys do in that situation?