Seeking Advice: My Boyfriend's (M27) Misinterpretations and his Infidelity with me (F25). What do I do?

My boyfriend and I have been dating for 8 months and live together. My boyfriend believes I am saying things that I haven’t said. For example, he thinks I told him, "I am going to continue cheating on you," even though I never said that. He also feels I am being "mean" to him and making hurtful comments when I am not. He believes that while we are at the grocery store, I am whispering "marry me" to men passing by, but I am not doing any of these things.

Despite this, he has cheated on me multiple times. I've discovered a dating app on his phone twice, and he was also caught agreeing to go out with another girl online. He claims that he started this "bad behavior" in response to me supposedly saying mean things to him. What should I do?

tl;dr