Notice to cease and notice to quit in owner occupied home

[Tayo Dare]

Hello, 

i rented out the 2nd floor of my owner occupied property ( I live on the 1st) in NJ and the tenants are habitually late with the rent. Ou residential agreement had a clause that stated two or more late payments within 4 months would be a violation of the agreement. i issued a letter to them last month informing them any further late payments would result in termination of the lease (which is now on a month-to-month. my question is, did my letter specifically have to say "notice to cease", or does explaining the terms and consequences in a late payment letter suffice? i sent a letter via certified and regular mail, and gave it to them in person. can a notice to quit be my next step?