A verb is used to express an occurrence, action, or state. It is the grammatical center of the predicate in a sentence.
An auxiliary verb is a verb which is used in the formation of tenses, moods, tones, etc.
Option A is correct as the sentence indicates the use for expressing necessity. Also, the subject is singular in the given sentence.
The other options are wrong as no other tense can be used here.
The correct answer is A) doesn't have to