I caught my boyfriend searching his ex for the third time

Problem/Goal: I caught my boyfriend searching his ex for the third time.

Context: The first time I (F27) caught him (M25), I confronted him and he told me na kaya daw niya ini-istalk kasi friends pa fb friends pa din ng ex niya yung family niya and gusto niya ipa unfriend sa pamilya niya, even re-assured me. But until now, friends pa din sila ng family niya. The second time I caught him, this January he lied. I already saw the name of his ex sa search list niya and when i tried to borrow his phone, hindi niya pinahiram agad which is strange. I caught him lying when I borrowed his phone again afterwards then wala na sa search list yung ex niya. I asked him if may tinago ba siya sakin, sabi niya wala. I confronted this to him earlier, I asked why he lied? He said ayaw niya daw makita ko kasi alam niya malulungkot ako. Ulul. The third time is nung isang araw, nasa search list nanaman ex niya. I asked him why, kasi curious lang daw siya sa life ni ex and sa new relationship ni ex. They broke up 4 years ago, kaya I asked him if he still have hang over feelings towards the ex pero sabi niya wala.Natural na curious daw siya sa lahat ng naging ex niya pero sinabi ko bakit yun lang palagi ko nakikita. He had another relationship after that ex then a fling. All before me. We became a couple almost a year ago. I gave him benefit of the doubt many times.

Previous Attempts: We tried talking again pero hindi naayos kasi nag spiral down siya na puro negative daw.

Alam kong natural lang maging curious pero yung paulit ulit and may lying na naganap? Hayy. I do knot know what to do.