Texting another girl, what do I do?

6 months ago my boyfriend left his phone out and a text from another girl came up so I went through the texts. He called her "baby" and "sexy" and she mentioned her being naked and he just said "ooh baby ooh baby" I confronted him and he said he didn't know why he did it. The girl lives 3,000 miles away and he met her when he was doing a summer job so I know he wouldn't have sex with her. But the texting is cheating he even admitted he considered it cheating. I decided to forgive him if he earned my trust back and in the last 6 months he has done just that. Whenever I ask to see his phone it's at random and there's nothing to see and he always gives his phone willingly but now whenever his phone buzzes my heart drops. In my heart I know he is sorry and won't do it again but I can't get it out of my head. What do I do?