YOU SAID:

The man went to the shop while walking his dog and bought some milk

INTO JAPANESE

男は犬の散歩をしながらお店に行き、ミルクを買いました

BACK INTO ENGLISH

The man went to the store while walking his dog and bought milk

INTO JAPANESE

男は犬を散歩させながら店に行き、ミルクを買いました

BACK INTO ENGLISH

The man went to the store while walking his dog and bought milk