Reply to "take a walk"

Hi David,

I have a question about 'taking a walk'. Here is an example:

A runs into B in a park one day and A asks B what he is doing in the park and then B answers A: I'm taking a walk around the park.

Is it correct to use 'taking a walk' here or should I say 'I'm walking around the park'?

Thank you very much for your help.

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