Tardily gathering how puzzle solvers think (9)

I believe the answer is:

laterally

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'puzzle solvers think' is the definition.
I can't tell whether this definition defines the answer.

'tardily gathering' is the wordplay.
'tardily' becomes 'late' (synonyms).
'gathering' becomes 'rally' (rally is a kind of gathering).
'late'+'rally'='LATERALLY'

'how' is the link.

Can you help me to learn more?

(Other definitions for laterally that I've seen before include "Sideways" , "Approaching the side" .)

I've seen this clue in The Independent.

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