End it or not?

I just found out a few days ago (while I was holding onto his phone e text came through) that my bf of has been send explicit texts to a girl he met through a friend of his and has met up with her once to fool around. I had asked him about somethings that made me think he was doing this, but he came up with an excuse everytime. He contends that, since he didn't have sex with her, then he didn't cheat. This is the 4th time he's done something like this and I'm at a loss for what to do, and I need to think about my 2 year old daughter. What should I do?

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