Thanks for the answer. I had already tried it with background text in the action loop, but it didn't help.
But.... I did a quick test now and thanks to your cool idea respectively the suggested workaround with changing the outfit and the narration text it worked!
I used narration text and checked it as background text. Thank you very much!
BTW. I searched the forum for this problem, but couldn't find anything yet. I wonder, that nobody else had this problem before. Having an independent loop-able action without any restrictions simultaneously to the ongoing game would be great.