Animating the ends of a lines along two different curves in aftereffects

I'd like to create an animation for a line in AfterEffects like this one: IMG_5034.TRIM.MOV - Google Drive

Notice how the end of the line is "attached" to the circle and follows its path, while the other side follows an arbitrary path. Both ends of the line move independently, both along different paths.

I'm wondering how I might go about implementing this in AfterEffects. I can create a line and animate its path, but I can't animate individual points of the path each along their *own* path. I could use the puppet pin tool to create a mesh of the line, but it gets distorted when I try to expand it. I could move the path frame by frame, but I'm thinking there might be a better way to do this.

Any help is appreciated, thanks!