いくべき

should continue to, should keep on

→ 行く
いく to go + べき Should; ought to
auxiliary · informal Rare #34,828
should continue to, should keep on Follows a verb in the て-form; いく can also add a sense of carrying an action onward or away.
JA: これからも日本語を勉強していくべきだ。
EN: I should keep studying Japanese from now on.
Conjugation of 行く

生き残った人間はきちんと生きていくべきです

Those who survived should live their lives properly.

— Godzilla Minus One (2023)

私はそこへ何を持っていくべきか母に尋ねた。

I asked my mother what I should bring there.

「身の回りの品をいくつか置いていくべきだな」とモーリスが言った。

“We should leave some of our belongings behind,” Maurice said.

人は情熱や感情を超えて生きていくべきだ

People should live beyond passion and emotion.

— 甘い生活 (1960)

医者たる者は最新の医学の発達についていくべきだ。

Doctors should keep up with the latest developments in medicine.