How can I reassure him it won't happen again?

I have a boyfriend Levi, he is funny, caring, thoughtful, attractive, an all-around amazing guy. I made a bunch of mistakes, using drugs and I cheated on him. I never want to cheat on him again, I have quit using, I have given him my phone, I don't use my Facebook and I have now moved in with him. What more can I do to reassure him that I'm not going to cheat again? I love him and he asked me to marry him and I said yes. but he keeps bringing it up everyday and saying what I slut I am and that I'm just going to do it again. when I have been showing change, and my capabilities of change.
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i didn't mention that in September he got really drunk and beat me up, he was blackout doesn't remember and I ran to my friend nathan, bad mistake he has always used and manipulated me and I guess I couldn't even go for support I made a mistake and I know it won't happen again. my boyfriend has quit drinking I live with him and we are doing great I just wanna keep proving myself to him. I just want to give him more reassurance it won't happen again if he goes away for the charges against him...
How can I reassure him it won't happen again?
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