Just casually amble out West (5)

I believe the answer is:

mosey

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'amble out west' is the definition.
'mosey' can be an answer for 'amble' (synonyms). I am unsure of the 'out west' bit.

I cannot understand how the rest of the clue works.

Can you help me to learn more?

(Another definition for mosey that I've seen is " Make off".)

I've seen this clue in the Evening Standard.

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