Hey Adelina,

Adding to Bicho's comment, I would recommend going with the flow in this kind of exercise. It's similar to impro in my head. In the sense that one has to accept what the other wrote and build on it.

which also means that when writing one needs to remember to live some doors open for the next one.

"you have to take that out" would be too much constraint, or would make it a different type of co-writing.