Lying cheat

So me and my boyfriend have been together about 18 months. In the first couple of months he was caught by a friend of mine kissing another girl in a club. When I confronted him about it the next day he said that he didn’t think he had done it but that he was so wasted he couldn’t even remember the night. We had some time apart but have been together since. We have lived together for about 6 months and this week he left his Facebook account open... I came across a chain of private messages between him and this girl. In the chain he had said to this girl that his girlfriend knew about the kiss and that they should keep it their secret. It has been over a year since this happened but now I know that he lied to me and was obviously not too drunk to remember the kiss, I don’t know what to do... Any advice would be appreciated! Thank you