My girlfriend has cheated on me and now she want a second chance with me. Not sure what to do?

Its recently come out that my girlfriend has cheated on me. I've suspected it for a few weeks but never been 100% sure. So on monday the chance came along to gather evidence in the form of snopping on her phone. There it was on her phone the evidence i needed to question her about it. I was away last weekend and suspected something my had happened while i was away as she wasnt responding to my texts for up to 3 hours at a time, which is not at all like her. I told her and looked at her phone and asked who this guy is and she burst into tears. I didnt shout or anything just listened to what she had to say. She explained she caught the train to his hometown and went to the seaside for the day. She admitted to kissing him and nothing else which i do believe. I'm fairly sure this was the first time they'd met. After the imital shock and sickness i felt i still feel like i love her and she wants me back but trust is going to be an issue now. I'm just really not sure what to do. Thanks for taking time to read. ay last weekend and suspected something my had happened while i was away as she wasnt responding to my texts for up to 3 hours at a time, which is not at all like her. I told her and looked at her phone and asked who this guy is and she burst into tears. I didnt shout or anything just listened to what she had to say. She explained she caught the train to his hometown and went to the seaside for the day. She admitted to kissing him and nothing else which i do believe. I'm fairly sure this was the first time they'd met. After the imital shock and sickness i felt i still feel like i love her and she wants me back but trust is going to be an issue now. I'm just really not sure what to do. Thanks for taking time to read.