mitwirken
to contribute
To take part in a shared task, project, or event and make a contribution to it.
Viele Freiwillige haben bei der Organisation des Stadtfestes mitgewirkt.
Many volunteers contributed to the organization of the city festival.

to participate / contribute
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to contribute
To take part in a shared task, project, or event and make a contribution to it.
Viele Freiwillige haben bei der Organisation des Stadtfestes mitgewirkt.
Many volunteers contributed to the organization of the city festival.

'Mitwirken' (to participate/contribute) is a separable verb. The prefix 'mit-' comes at the end in a main clause. In the infinitive with 'zu', 'zu' comes between 'mit' and 'wirken'.
Er wirkt an dem neuen Theaterstück mit.
He is participating in the new play.
The verb 'mitwirken' (to participate/contribute) is usually used with the prepositions 'an' or 'bei' and the dative to name the project or activity.
Zahlreiche Künstler wirkten an der Ausstellung mit.
Numerous artists contributed to the exhibition.
The preposition can make the meaning more precise. 'An' or 'bei' einem Projekt mitwirken means to participate in a project. 'In' einem Film oder Stück mitwirken means to appear or perform as an actor or performer.
Sie hat an einer wichtigen Studie mitgewirkt.
She contributed to an important study.
'Mitwirken' (to participate/contribute) is a rather formal word that is often used in official, professional, or artistic contexts.
Wir danken allen, die am Gelingen dieser Konferenz mitgewirkt haben.
We thank everyone who contributed to the success of this conference.
to play
'spielen' and 'mitwirken' can both fit when talking about theater, film, or other shared projects. Use 'spielen' when someone portrays a specific role. 'mitwirken' means more generally that someone is involved in a performance, film, event, or project and makes a contribution. For actors, 'mitwirken' can also mean that they appear in a film or play. However, it sounds more formal than 'spielen' and does not necessarily name the exact role. The words can be confused when talking about a film or a play: 'spielen' emphasizes the role, while 'mitwirken' emphasizes participation.

An dem Schulprojekt wirken auch mehrere Eltern mit.
Several parents are also contributing to the school project.
Lisa spielt in dem Theaterstück die beste Freundin der Hauptfigur.
Lisa plays the main character's best friend in the play.