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to go in the direction of; to proceed toward; to proceed according to; to repair to; to betake oneself to
to become; to face (facts, circumstances, etc.)
時代の流れは国際化の方向に趨いている。
The trend of the times is moving toward globalization.
議論は次第に合意へと趨いていった。
The discussion gradually moved toward consensus.
経済は回復の方向に趨いていると見られる。
The economy is seen as trending toward recovery.