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finally; in the end; at last
in the end; after all; never (happened)
長年の夢だったマラソンを遂に完走した。
I finally completed the marathon, which was my longtime dream.
探していた手紙はついに見つからなかった。
The letter I was searching for was never found in the end.
遂に彼女は自分の店をオープンできた。
She finally opened her own store.