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The sleeping with someone else thing is a bit different. It depends on the circumstances, if he slept with somebody the day after you broke up then it is a negative reflection of his character. However if a period of time had elapsed than he was free to do so, providing he wasn't leading you on about getting back together when he slept with the other person.
So if you can get past the sleeping with somebody else element you just have to really analyse why you broke up. There were reasons for the breakup, sometimes those reasons may have been wrong. If they were good reasons to break up then they will resurface once the happiness of getting back together starts to die down. Maybe you have both changed and the reasons you broke up aren't an issue any more. I don't know the reasons so I can't make a judgement on that.
But those are the two things you need to analyse. Was it acceptable him sleeping with somebody else? And have things/people involved changed enough to ensure that the old problems with the relationship won't resurface?
Hope this helps and you make a decision you are happy with. Like I said I went through something similar so if you want to discuss it more feel free.
What was going on..... How long had things been not right?..... Has anything truly changed?
I would take some time to sort through it all and I wish you well......xo