Just cut ties, but how to handle mutual friends?

So after being the emotional blanket for too long I decided to cut ties with my ex. Not forever, because we were great friends beforehand, but for the betterment of our friendship. up until this point we remained friends, but it was unfair how we treated each other. I do not exclude my actions and mixed signals that I have sent her way. The big concern I have is that we share a lot of CLOSE mutual friends. Her friends are my friends, and my friends are hers. we are all very close. Just today one of her longest and closest friends hit me up to talk about relationship problems she's been having. I have always been that great listener and supporting person to any person I consider a friend. I heard her story and gave her my advice. She then asked me to go out for a drink so we can talk more about it. I know its harmless, but I'm unsure if I should. I'm unsure if I should continue talking to some of these people while I have ties cut with my ex. I don't want my ex to take our meeting the wrong way, and I don't want things I may say to get back to my ex, at least during this initial period. I have thought about just telling her friend my decision, and hope she does not relay it back to her. My main focus on cutting the ties is NOT letting my ex know anything. complete shutdown.

what do you think is a plausible way to handle this?
Just cut ties, but how to handle mutual friends?
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