YOU SAID:

I go out to buy groceries then I come home and drink a cup of tea

INTO JAPANESE

私は食料品を買いに出かけ、家に帰ってお茶を飲む

BACK INTO ENGLISH

I go out to buy groceries, go home and have tea.

INTO JAPANESE

私は食料品を買いに行き、家に帰ってお茶を飲みます。

BACK INTO ENGLISH

I go shopping for groceries and go home for tea.

INTO JAPANESE

食料品を買いに行って、お茶を飲みに帰ります。

BACK INTO ENGLISH

I go shopping for groceries and go home for tea.