Simple or compound sentence

What makes the following a simple sentence?

James cleaned and polished his brother's car.

Isn't this a compound sentence made of two simple sentences

"James cleaned his brother's car." and "James polished his brother's car."?

Solution 1:

"James cleaned and polished his brother's car".

It's a simple sentence because it only contains one independent clause, i.e. the sentence as a whole.

It does, however, contain a coordination of two verb phrases, so the structure is:

"James [cleaned __ ] [and polished __ ] his brother's car".

Both coordinates contain a 'gap' __' (representing the objects of the verbs) co-indexed with the NP "his brother's car" in postnuclear position.