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finally; in the end; at last
in the end; after all; never (happened)
十年かかってついに夢が実現した。
After ten years, the dream finally came true.
ついに雨が止んで青空が見えてきた。
The rain finally stopped and blue sky appeared.
何度も挑戦してついに合格できた。
After many attempts, I finally managed to pass.