I don't necessarily disagree with Gucci's advice. It can make sense if there is OM/OW. If there is OM/OW, saying it's not working is pretty obvious. However, I also believe you need to be careful with how the filing is handled, etc.
When my W started talking about divorce, I did not fight it, but I made it clear she wanted it and I didn't. I agreed with my C that I needed to put the full burden of the decision on her. She wasn't willing to talk about it at first, too much anger. But after a few weeks, she was willing to talk and she became ready for MC.
I do not believe you just "move on" to someone else, or even give the impression of that. My W did not have or seek out OM, but I was given some advice by a divorced friend. He said he regretted starting to date after his W asked for divorce. He said in his case it really hurt the possiblity of reconciliation.