What is the past-tense verb for be?
The verb is still "to be", regardless of the tense. It is an irregular verb, and the past tense forms are was for I and he/she/it, and were for we, you, and they.
Was and were.
The verb 'am' is not an action verb, 'am' is a form of the verb 'to be', for example: I am...; you are...; he, she, it is...; we are...; they are... The verb 'am' can be a linking verb in a sentence, for example: I am tall. The verb 'am' can be a helping verb in a sentence, for example: I am drinking tea.
Some words can function as either a helping verb or a linking verb, but a linking verb and a helping verb are not the same thing. A linking verb stands alone as the main verb and links the subject to the predicate nominative or predicate adjective. A helping verb is not the main verb and helps the main verb. (A helping verb is also known as an auxillairy verb.)