Back and forth relationship - moving on with new guy but the old one comes back. What to do?

My boyfriend packed up and left after stupid argument saying that we finished. This is the 4th times he left and abandoned me over small insignificant arguments. The other times, he came back after a day or two. This time it has been a week.
I started chatting with others on a dating site, gave my number and agreed to meet a new guy. Then 3 days after that my boyfriend wants back after a week of abandoning me.

What should I do?
Yes I still have feelings for him but I agreed to meet this new guy & given my number already.
I want stable relationship and I told him several times that I don’t want someone who just walk away when things are getting difficult.
Back and forth relationship - moving on with new guy but the old one comes back. What to do?
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