How to make interactive video presentation? I need to make presentation, which will be used as background for stage play. 

I work with After Effects and Premiere better, than with PowerPoint. And I see more possibilities in them. I can make better result in video editing software, then in PowerPoint. So it wold be great to find way, to make presentation in them. 

Because it can take different amount of time for actors, to reach next "slide" in my "background presentation", I can't just make seamless video.

How I see it, each presentation "slide" can be made with endless loop of video, and at the click/keypress video should go to the next video-loop.

One variant is to make PowerPoint presentation with separate video in each slide... But PowerPoint work with videos pretty badly, how I remember.

What is the best way to accomplish my goal?

Thank you in advance!
Quickest way is to create each video with multiple repeats rendered in one file, enough to cover a worst case scenario. Queue these in a playlist in VLC, Potplayer ...etc and manually advance as necessary.

You may also want to look at video jockey (VJ) apps like LiVES. Since those are meant for interactive video manipulation and playback, they may have this functionality.