In a manner that shows willingness to listen, cooperate, or adapt; in a receptive way.
From 'amenable' plus the adverb suffix '-ly'. This adverb form describes how someone behaves when receptive to influence or cooperation.
When you 'amenably accept' a compromise, you're genuinely willing—not just grudgingly going along. It's the difference between 'fine, whatever' and actually being open to the idea.
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