The Next Steps
If you want to save the relationship, the next step is to own up to your mistakes. There's no use in denying it because you've been caught red-handed. Your partner has proof of you cheating on him, so be honest. Admit to the dirty deed and beg for forgiveness. A lot.
You need to prove to your man that he truly means the world to you. Explain that what you did was a huge mistake that will never happen again. Stress the fact that you will do what it takes to make the relationship right again.
Most people who have been cheated on feel bad about themselves because they feel that they can't give the cheater what they want, or that they somehow contributed to the cheating. So you need to make sure your man knows what a good guy he is and that he is not at fault for your actions.
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Follow your guy's cues. Some people need a break to think about the relationship and help rebuild their trust in the other person. If he needs some time apart, give him some space. If he wants to spend even more time with you, it may be because he's afraid to leave you alone.