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How would I make it that the frame of an actor's animation only changes when I change the animpos variable, but it stays where it is once it's been set?

You can when changing animation set the animation state to STOPPED. If you want this to happen immediately, in the actor's create actor event, use ChangeAnimationDirection("Event Actor", STOPPED). With that the animation won't play, and setting animpos will do what you want.

Yay, thank you!
That was one of the most annoying bugs in my game.