어 나서다

set out to do something

나서다 is stepping out to take something on, and most of these lines pair it with the verb for seeking: setting out to find a hospital in a hurry, internet sleuths setting out to find the culprit, a team setting out to find other food, a scientist who set out to track down a bug. It also stands alone as stepping up, in the line saying it is the carmakers' turn to act for us, and paired with following it means coming along.

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