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to entrust (to someone); to leave (in someone's hands)
この重要なプロジェクトは君に任すことにした。
I've decided to entrust this important project to you.
細かい作業は部下に任すようにしているよ。
I make it a point to entrust detailed work to my subordinates.
運を天に任すしかない状況に追い込まれていた。
I was driven into a situation where I had no choice but to leave it to fate.