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to penetrate; to sink in
to devote oneself (to); to do intently and exclusively
to do throughout (e.g. the night)
彼は一晩中仕事に徹することもよくあります。
He often devotes himself to work all through the night.
彼は会議中ずっと聞き役に徹していた。
He stuck to the role of listener throughout the meeting.
役者は舞台上で役に徹して演技を見せました。
徹する was important.