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First thing after dinner, I've ended up saying goodbye (5)

Ross

I believe the answer is:

adieu

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'goodbye' is the definition.
(synonyms)

I don't understand how the remainder of the clue works.

Can you help me to learn more?

(Other definitions for adieu that I've seen before include "Farewell (French)" , "Farewel" , "Vale" , "Bye" , "the last word in France" .)

I've seen this clue in The Irish Times.
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