~어/아/여/해야지 (~eo/a/yeo/hae-ya-ji) – (someone) should or must do this
You would typically use ~어/아/여/해야지 to tell someone about the need to do something, usually also known by the listener but you want to emphasise and give advice.
~어/아/여/해야지 is considered a cordial and informal phrase so even adding 요 behind would not make it extremely polite for someone you’re seeing for the first time.
Try not to use ~어/아/여/해야지 in your conversation with someone either older/elder than you or someone whom you need to respect.
Examples: 엄마 날마다 일찍 일어나서 아침을 준비하니까 엄마를 섬겨야지.
Your Mom wakes up early every day and prepares breakfast for you so you need to take good care of her.
물론 일이 중요한데 일이 끝난 후에 바로 집으로 가서 푹 자야지.
Of course work is important but right after your work is over, you must go home and rest well.