Should I take her back or no?

Here's the background:

My girlfriend and I have been dating for 5 years. I was on the verge of asking her to marry me. The past couple months I've been busy with work and getting my degree in college. She's been hanging around with friends that to me aren't the beast crowd to hang out with, being cheater and alcoholics themselves. She went out to bars and clubs and it increasingly got to the point where when I had time to see her she was out partying. Well...come to find out she's not this person I used to know and I think it all stems from her friends. I've found evidence around her house leading to things that happened and she tried hiding it form me (most likely because she didn't want me to find out of course. )She ended up one night cheating on me while liquored up. I had confronted this about her and asked some very basic questions...Do you still love me (yes)...do you regret it (yes)...was this planned or did it just happen (wasn't planned)...she is devastated that she did this and she blames only herself. Where everything stands now is that she needs to "find who she is" and what she wants out of life and that we just need to take break it off for a while.

My head says that I can't accept her back...but my heart thinks that it was mistake...she was drunk..she didn't know what she was doing and that everyone is human and people make mistakes no matter how dire they are. I still love her to death. Like I said my head says no (once a cheater always a cheater) and my heart says to forgive and to work through this. Relationships aren't based on the good times but how they are through the absolute worst of times.

I just needs some advice on how to deal with this and what I should think about doing.
Should I take her back or no?
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