Your explanations, while fine, seem somewhat rather complicated. Here's a quicker way.
How to find an action verb in a sentence:
Go word by word and ask, "Is that something a person can do?" If the answer is Yes, then it's an action verb.
How to find a linking verb in a sentence:
First, learn the list (Click here). Second, perform a substitution test:
If you can replace the verb with a form of the verb "to be" (is, am, are, was, were, be, been, or being), and the sentence still makes sense, the verb in the sentence is a linking verb. If it does not make sense to replace it, the verb in the sentence is an action verb.
Process for finding the verb or verb phrase in a sentence:
Look for a word that shows action in the sentence.
Double-check to be sure the word is the action in the sentence. (Ask yourself, "Is someone or something doing that in this sentence?")
If "yes," double-underline the word and label it "A" for action verb. Now skip to the sixth part of the process. If "no," look for a linking verb.
Perform the Substitution Test to be sure it is linking and not action.
When you are sure the word is a linking verb,
double-underline it and label it "L" for linking verb.
Look at the words that appear before
the main verb
(your “A” or “L”) in the sentence. Are any of them
on the list of helping
verbs? If so, double-underline
each of them and label them "H" for helping verb.
What is a verb? (Linguistics)
What Is a Verb?