In syntax, why cannot we say things like
"he took walked at the park"?
but can say things like
"he took a walk at the park"?
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A walk at the park is essentially acting as a noun phrase where the word walk is not the verb to walk but the noun walk which is a thing that people do.
Therefore, in this whole sentence, there is only one verb: Took. This verb takes the past tense of take to be took.
So, applying that knowledge to this sentence in particular:
He took a walk at the park.
Subject(He) Verb Object(noun phrase)
agrees with English syntax