Walk to gym in smooth flat land (6)

I believe the answer is:

steppe

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

'smooth flat land' is the definition.
'steppe' can be an answer for 'land' (steppe is a kind of land). I also know that 'flat' relates to this answer.

'walk to gym' is the wordplay.
'walk' becomes 'step' (I've seen this in another clue).
'to gym' becomes 'pe' (Physical Education).
'step'+'pe'='STEPPE'

'in' acts as a link.

Can you help me to learn more?

(Other definitions for steppe that I've seen before include "Edxtensive plain" , "plain territory" , "crosses Siberia" , "Large treeless area of Siberia" , "Flat area of eastern Europe or Russia" .)

I've seen this clue in The Sun.

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