I caught my boyfriend sexting another girl

Please no negative or rude comments, I am looking for advice. thank you advance!

Quick background, I have ave been with my boyfriend for over 6 years, with live together, very serious relationship. We did break up over a kind of similar situation like this 3 years ago then got back together.

Fast forward, I was getting ready for work Tuesday morning and I saw his phone sitting on the island in the kitchen. I grabbed it and was going to give it to him before I left for work (he was still sleeping). I saw a message from a girl, we will call her Britney, that I’ve had issues with in the past. I immediately got upset/sad. I opened up his phone, I knew the password, and went straight to their messages (I never go through his phone however I did this time bc I saw this particular person on there). So what do I see. I don’t see any photos exchanged, but there’s plenty talk of them texting sexually, about how she wishes she could have had sex with him when she had a chance, he wishes he could have done i when he had the chance 3-4 years back (they open stores for the company they work for, that’s how they met), he was talking about he wants to fly out to see her.

I did obviously confront him after work. He cried, apologized and won’t stop saying sorry to me.

So I’m basically asking, I don’t know what to do and I’m really pissed off and obviously really upset. I feel like in a relationship, in my opinion that’s a form of cheating. Have you ladies or guys ever been through this? What did you do? Do you guys think that’s a form of cheating or am I overacting and should I just lay off.