Crossword Genius

Left over fag rolled — it helps me think clearly (5)

Ross

I believe the answer is:

logic

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

'think clearly' is the definition.
The answer and definition can be both related to thinking as well as being singular nouns.
Maybe there's an association between them I don't understand?

'left over fag rolled it helps me' is the wordplay.
I cannot really understand how this works, but
'left' could be 'l' (common abbreviation) and 'l' is found in the answer.
'over' could be 'o' (cricket abbreviation) and 'o' is located in the answer.
'me' could be 'i' and 'i' is located in the answer.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for logic that I've seen before include "Rationale ?" , "Chain of reasoning" , "Reasoned argument" , "The science of reasoning from cause to effect" , "this makes sense" .)

I've seen this clue in The Guardian.
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