I love him and want to give him a second chance... should I?

Anonymous
Hi. So, I met this wonderful guy and we dated for four months. He was affectionate, loving, respectful, etc. and the relationship was perfect, until he blindsided me with an unfaithful act. Long story short, I discovered that he had a sexting fling (it only happened once, as the person he sexted with contacted me when they found out he wasn't single and told me everything). My ex admitted to it and was very apologetic and spiraled into depression and self loathing. I broke up with him right away but we started talking some weeks later. He promised that he'd never do it again and work to earn my trust back. The trust I had was destroyed and it made me anxious and paranoid, so I cut him off for two weeks completely.

Just the other day I messaged him saying I did so to give myself time and space, and that I needed more of it. He said to take my time and that he didn't want me out of his life, and that he'd been struggling emotionally too and would use the time to work on himself. It was a long distance relationship and I don't know if I should give him another chance because we're far apart and it would be harder for me to know he's telling the truth. On the other hand, he never gave me a reason to doubt his loyalty before all of this. He would always tell me he loved me and didn't have any problem telling others that too (especially on social media). He wasn't flirty with other girls from what I saw. He also said he didn't feel like anything was lacking in our relationship and that he had a momentary lapse in self control. That's what I'm unsure about, though I haven't yet given him a chance to prove himself.

What do you guys think? Also, as I take time out (It's been several days since our last contact and I want to take at least a month to heal), what suggestions do you guys have to help the heartache/extreme longing? Lastly, what behavior do you think I should look for in someone trying to prove their loyalty in a long distance relationship? Thanks so much.
Updates:
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PS. I will also add that I didn't tell him I wanted to give him a second chance yet. As far as the sexting thing, the other person was the one who pursued him. My issue was that he didn't stop that person, and even though he did not reciprocate as much he still encouraged that behavior. I let him watch porn and we'd sext a bit to get each other off, I just didn't want him sexually or romantically interacting with another individual.
I love him and want to give him a second chance... should I?
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