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do one's (level) best
to do something as well as one can. Just do your level best. That's all we can ask of you. Tom isn't doing his best. We may have to replace him.
do your (level) best
to try very hard Tickets are hard to get, but I'll do my best to find you one. Work is easy - you show up in the morning, do your level best for eight hours, then you go home.