Pokes gently with sticks (5)

I believe the answer is:
'pokes' is the definition.
('prod' can be a synonym of 'poke')
'gently with sticks' is the wordplay.
'gently' becomes 'p' (I've seen this in other clues).
'with' is a charade indicator (letters next to each other).
'sticks' becomes 'rods' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'p'+'rods'='PRODS'
Can you help me to learn more?