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to chase; to run after; to pursue
subsequently; following that; (and) then
犬が公園で猫を追い掛けていた。
A dog was chasing a cat in the park.
バスに乗り遅れて走って追い掛けた。
I missed the bus and ran to chase it.
夢を追い掛ける若者の姿に心を打たれた。
I was moved by the sight of young people chasing their dreams.