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to chase; to run after; to pursue
subsequently; following that; (and) then
逃げた犬を追い駆けて公園まで走った。
I ran to the park chasing after the dog that got away.
バスを追い駆けたが間に合わなかった。
I chased after the bus but didn't make it.
夢を追い駆けて故郷を離れた。
I left my hometown to chase my dreams.