Should I tell my ex/friend about my date?

I was in a situationship with a guy who was on verge of breaking up with his girlfriend. Obviously, he couldn't, so I broke it off with him instead. I still love him but I know he doesn't have the guts to end it with his girlfriend. Clearly, he is still in love with her as well. But he wants to stay friends with me. We work in the same office and it's hard to avoid so I agreed on being friends. He says he still has feelings for me, but we both are not acting upon our feelings because I know nothing will happen unless he leaves her. Anyway, even though I still have feelings for my ex, I am open to dating now, and I think I can go out with another colleague of mine.

Should I tell him that I am not waiting around and going on a date with the other guy? Or do I not need to broadcast my every move because we are over and done with anyway? Would it come off as if I am hiding the truth?

Should I tell my ex/friend about my date?
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