Why did Lord Rama worship Lord Vishnu when he (Lord Rama) himself was Lord Visnu?

Why did Lord Rama worship Lord Vishnu when he (Lord Rama) himself was Lord Visnu? Lord Rama, though was Lord Vishnu himself, worshipped Lord Vishnu. Lord Vishnu incarnated as Rama on the earth. This was a human form of the Supreme Lord (Though a human form, but was away from all flaws. The same Vishnu, who possesses infinite and complete joy, knowledge and bliss came on earth as Rama. His ). As the Sanskrit shloka goes, “Martyavataare hi tu martyashikshanam”, which means “Lord appears as a human for teaching the human, how to lead a good and a successful life”, Lord Rama also worshipped Lord Vishnu (SriRanganatha Swamy) in Ayodhya under the guidance of Maharshi Vasistha, to teach that one must worship Lord Vishnu. He doesn’t need to worship himself actually, because he himself is Vishnu. Talking about other devatas like Brahmaji, Shivji, etc. Rama worshipped them just to teach us that worshipping them is also important. Lord Vishnu never gets pleased if you don’t worship his devotees like Lakshmi, Brahma-Vayu, Saraswati-Bharati, Garuda, Aadishesha, Lord Shiva, etc. along with Lord Vishnu considering Srihari as the supreme and others as his devotees. SriRama doesn’t need to worship anyone because all these devatas themselves worship him with pure devotion. One must note here, that Lord Rama is Lord Vishnu himself and he worshipped himself, just for “Loka Shikshanaartha” (teaching us).