That spring, the team should have been training for the summer games ahead. What is the sentence's complete action verb?

Based on the given sentence above, the complete action verb would be "should have been training". When we say action verb, this is the type of verb that serves as the main verb in the sentence for it tells what the subject is doing or what the subject is all about. This is the complete action verb because the tense is included to make the verb understandable as to when the action actually happened.