Act back and forth (4)

I believe the answer is:

deed

I believe this is a double definition.

'act' is the first definition.
(deed is a kind of act)

'back and forth' is the second definition.

(Other definitions for deed that I've seen before include "Heroic exploit" , "Legal document for transfer of property" , "documentary evidence" , "Something done" , "Intentional action" .)

I've seen this clue in The Guardian.

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