die Verabschiedung
farewell
The act of saying goodbye to someone who is leaving or leaving a position.
Die Verabschiedung von unserer Austauschschülerin war sehr emotional.
The farewell to our exchange student was very emotional.

farewell / adoption
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farewell
The act of saying goodbye to someone who is leaving or leaving a position.
Die Verabschiedung von unserer Austauschschülerin war sehr emotional.
The farewell to our exchange student was very emotional.

'Die Verabschiedung' (the farewell/adoption) is the noun derived from the verb 'verabschieden' (to say goodbye/to pass a law/to retire someone). The different meanings of the noun correspond to the uses of the verb: sich von jemandem verabschieden (to say goodbye to someone), ein Gesetz verabschieden (to pass a law), or jemanden, e.g. in den Ruhestand, verabschieden (to send someone off, e.g. into retirement).
Das Parlament wird das Gesetz nächste Woche verabschieden.
Parliament will pass the law next week.
The context shows which meaning is intended. If it is about politics, it usually means the passing or adoption of a law. If it is about people leaving a place or position, it means a farewell.
Die Verabschiedung des Haushalts dauerte die ganze Nacht.
The adoption of the budget lasted all night.
In the political or legal meaning, the noun is almost always used with an object in the genitive. Typical combinations are 'die Verabschiedung eines Gesetzes' (the adoption of a law), 'des Haushalts' (of the budget), or 'einer Resolution' (of a resolution).
Die Opposition stimmte gegen die Verabschiedung des Gesetzespakets.
The opposition voted against the adoption of the package of laws.
When a person is ceremonially released from an office, people often speak of the 'Verabschiedung in den Ruhestand' (farewell into retirement). This is a fixed expression for the end of a professional career.
Die Firma plant eine große Feier zur Verabschiedung des Direktors in den Ruhestand.
The company is planning a big celebration for the director's farewell into retirement.
assumption / acceptance
'die Annahme' and 'die Verabschiedung' can both refer to the formal adoption of a proposal or law. 'die Annahme' emphasizes that a proposal is accepted or approved. 'die Verabschiedung' is used especially for laws, budgets, or resolutions and refers to the final official step by which something is passed. The words can be confused because they appear similar in political or formal texts. 'Annahme' fits more with approval; 'Verabschiedung' fits more with the official passing of something.

Die Verabschiedung des neuen Gesetzes ist für Freitag geplant.
The adoption of the new law is planned for Friday.
Nach langer Diskussion stimmte der Ausschuss für die Annahme des Antrags.
After a long discussion, the committee voted in favor of adopting the motion.