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to be in charge of; to manage; to direct; to administer; to preside over
to rule; to govern; to control
伝統行事を司る役目を任されました。
I was entrusted with the role of presiding over traditional events.
彼は長年この部門を司ってきた人物だ。
He is a person who has governed this department for many years.
彼は部署全体の予算管理を司っている。
He oversees the budget management for the entire department.