Cheated on my girlfriend?

i cheated on my gf by hooking up with a girl in mexico on spring break. We were both drunk but did it two nights in a row. I didnt mean anything and I didnt even know her name. I kept it a secret for a like 4 months in fear of my gf dumping me. I recently told her and shes crushed but niether one of us want to break up cuz we have been together so long. However, we think that something needs to be done as a disciplinary action, any ideas?