If a man is keeping his options open should you do the same?

He started dating another girl in the past month but he stares at me, watches me talk to other men, he teases me, flirts with me, the other night he grabbed my hand and began stroking/rubbing my hand in front of the girl he is dating (I’m not sure if she saw it). Also he claims not to remember this incident. So if he is “keeping his options open” should I do the same?
If a man is keeping his options open should you do the same?
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