Girl's Behavior

How do I prove to my girlfriend that I trust her?

Me and my girl broke up last Sunday because she thinks ii don't trust her. Last Saturday night she was at a party and I got word from what was a friend that she was messing around with some other guys and that she was drunk. Well to make it short I became infuriated and didn't talk to my girl until I could verify everything. and it all turned out to be a lie, born out of jealousy .

This is the second time something like that had happened, and I understand her anger over me not trusting trusting her, she even called me cynical.. I apologized for what happened and I am deeply sorry for what had happened,But she gave me only one way to win her back, which is for me to prove to her that I trust her. and I honestly have not one clue on how to do that , other than promising her that I do. Any advice would be appreciated
How do I prove to my girlfriend that I trust her?
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