to actively pursue one's ambitions or desires
自分の夢や野望を積極的に追い求める (jibun no yume ya yabō o sekkyokuteki ni oimotomeru)
"He left his hometown to chase after his dreams of becoming an entrepreneur."
"彼は起業家になるという夢を追い求めて故郷を離れました。" (kare wa kigyōka ni naru to iu yume o oimotomete kokyō o hanaremashita)
to clearly define goals or intentions
to keep the door open for someone as a polite gesture
to stay until the end of something that is long or boring
to make a tense or angry situation more peaceful
to yield to temptation or pressure
to reduce a student’s grade for an error
