My boyfriend cheated

Well I was using his phone and ended up going thru it and I see he message some naked model on reddit asking her name. It looks like she lives in Hawaii where we live and maybe even goes to the gym he goes to. Anyway I doubt she’d ever message him back it hurt me that he did that and I also saw he looks at sexy flight attendants and nurses and phat ass Asian girl. It’s just insane to see what he looks up and likes and what turns him on. I feel so hurt and he said so what do you want to do then? I’m thinking he actually wants to break up when he doesn’t even say sorry just asks what I’m going to do about it. I started crying and he said “don’t cry it’s not worth it” he said he’s stupid and wish he could go back and not do it. Ughh I feel like he could do much worse now? I don’t want to feel like i need to look through his phone... I don’t want that. Is it harmless? Should I feel ashamed? Should I leave??? I don’t know what to do. My heart aches but for some reason I’m not mad it hurt