Tā cháng xiù shàn wǔ, hěn kuài dǎkāi le wàijiāo júmiàn.
She was adept at diplomatic maneuvering and quickly opened up new relationships.
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From 《韩非子·五蠹》: '长袖善舞,多钱善贾' — 'long sleeves help you dance, plenty of money helps you trade.' Originally described having resources to work with; modern usage emphasizes personal networking and social skill, sometimes with a hint of opportunism.
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Can be complimentary (deft networker) or slightly pejorative (operator, schmoozer). Context decides.