Crossword Genius

Manage marathon, one in Paris following river (3)

Ross

I believe the answer is:

run

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This clue is a quadruple definition!!

'manage' is the first definition.
(both can mean to organise)

'marathon' is the second definition.
(thesaurus)

'one in paris following' is the third definition.
The answer and definition can be both acts as well as being singular nouns.
Perhaps there's an association between them I don't understand?

'river' is the fourth definition.
(thesaurus)

Can you help me to learn more?

(Other definitions for run that I've seen before include "Unbroken series" , "Discharge" , "Organise - series" , "Manage (eg, a company)" , "Organize" .)

I've seen this clue in The Times.
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