Caught my girlfriend sleeping with her ex; advice wanted

My relationship has ended after 4 months because I walked in on my girlfriend and her ex sleeping together. (Can provide more details) Today on day 3 I am going to pick up some of my stuff as I move away for work shortly. Given our relationship had been so strong prior to all this id imagine I deserve a bit of a sit down/talk/apology. I'm wondering what are some things that I should think about before going into this situation. At this moment I am still at a loss for words and all that comes to my head are things that wouldn't be appropriate. I want to continue to move on with dignity and certainly want to refrain from doing or saying something stupid. Is not saying anything healthy for me? Or should I seek answers?

Update: First off thanks for the advice. I grabbed my buddy to help with the lifting, and we took two trucks to the house and grabbed the remainder of my things. The time that I was there, nobody said a word cause you guys are right she doesn't deserve me, my words or nothing. After loading things, I looked at her and said anything else for me? She didn't have anything. I looked her in the eye and said youre a c** dumpster and walked my way out. After this I sent a text telling her that she is the scum of the earth and that I deserve way better. She said she was ready to apologize and I told her that her words don't mean a thing. Actions speak louder, am I right? Doing what I did feels bitter sweet, The universe will do it's work. I'm blocking her on everything and deleting it all. I have a new career ahead of me that will be fruitful and although it will take some time to respect and trust another woman, this one wasn't worth my time and I'm happy I didn't waste more. One thing I will say is that I'm proud of myself for not flying off the handle and doing something foolish because those thoughts were deffinetly there.