Left-of-centre sorts often fail to think things over (7)

I believe the answer is:

reflect

I'm a little stuck... Click here to teach me more about this clue!

'think things over' is the definition.
'reflect' can be an answer for 'think' (reflecting is a kind of thinking). I'm unsure of the 'things over' bit.

I can't explain the rest of the clue.

Can you help me to learn more?

(Other definitions for reflect that I've seen before include "Meditate - mirror - show" , "shed" , "Think or mirror" , "chew the cud" , "Cogitate" .)

I've seen this clue in the Sydney Morning Herald.

Want a hint initially instead of a full solution? Install my app