Crossword Genius

Second stick tossed in river (6)

Ross

I believe the answer is:

depute

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'second stick' is the definition.
Although both the answer and definition are verbs in their base form, I don't see how they can define each other.

'tossed in river' is the wordplay.
'tossed' becomes 'put' (I can't justify this - if you can you should believe this answer much more).
'in' is an insertion indicator.
'river' becomes 'Dee' (River Dee).
'put' inserted within 'dee' is 'DEPUTE'.

Can you help me to learn more?

(Other definitions for depute that I've seen before include "Delegate to, appoint as representative" , "Appoint to act on one's behalf" , "Delegate task to someone" .)

I've seen this clue in The Times.
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