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You're wrong. A finite verb is a verb conjugated for tense at least, and perhaps number and aspect, that may be used as the main verb of a sentence.

I visited the lady.

An infinitive is a vebal noun that retains the ability to receive objects and adverbs.

What I did was visit the lady momentarily.

What I planned was to visit the lady momentarily.

As for running, it can be a gerund (somewhat like an infinitive):

Running is good for you.

It can be a participle, which is a special sort of adjective that may take an object or an adverb:

You are running a risk unnecessarily.

It can be a full-fledged adjective:

There is running water.

But if you say, "Running is in the dictionary," you should italicize.
The first thing we did was take a survey.

Of course take a survey is a predicate noun, but that doesn't change the fact that take is an infinitive. Infinitives are nouns.

An antecedent is only a word that comes before another that refers to it. The words can be any distance away from each other.
Students: We have free audio pronunciation exercises.
drew.wardwhat makes you think there is a special construction involving 'do'?
It's special, because no other verb behaves like that.

drew.wardI (subject) do (aspectual auxiliary) take (vector) surveys (object).
English verbs have three aspects:

Perfect: I have taken, I had taken, I will have taken

Progressive: I am taking, I was taking, I will be taking

Gerundive: I am going to take, I was going to take, I will be going to take

There are other names for the aspects, and other constructions, but none of them involve 'do'. So 'do' is not an aspectual auxiliary.