From what I understand 들어가다 means "to go inside" (with 들어오다 meaning come inside)
But I have seen conversations like this is basic Korean books:
가: 먼저 들어가겠습니다. 안녕히 계세요.
나: 안녕히 가세요. 조심히 들어가세요. 내일 봅시다.
How is 들어가다 a farewell greeting? When I look up 들어가다 in English to Korean dictionary, non of the meanings seem to be a farewell.
What exactly does it mean as a farewell? What is the word root?