Answer:

To understand why option 'A' is the correct answer, let's analyze the given sentence and the four options provided.

The sentence structure is as follows:
Subject + Auxiliary Verb + Main Verb + Object

In this case, the subject is "I" and the main verb is "taking." We need to choose the correct auxiliary verb to complete the sentence.

Option A: am taking
This option uses the present continuous tense. It indicates an action that is happening in the present or in the near future. Since the sentence mentions "next week," it suggests that the action of taking a few days off will happen in the near future. Therefore, this option is correct.

Option B: will have been taking
This option uses the future perfect continuous tense. It indicates an action that will be ongoing and complete in the future. However, this tense is not suitable in this sentence because it implies a continuous action that starts in the future and continues until a specific point in the future. It does not match the given sentence structure and the intended meaning.

Option C: shall have been taking
This option also uses the future perfect continuous tense, but with the auxiliary verb "shall" instead of "will." The usage of "shall" is less common and often used in formal or literary contexts. Similar to option B, this tense does not match the given sentence structure and intended meaning.

Option D: had taken
This option uses the past perfect tense. It indicates an action that happened before another past action or a specific point in the past. However, in the given sentence, the action of taking a few days off is mentioned as happening in the future (next week), so this option is not appropriate.

Therefore, the correct answer is option 'A' - "I am taking a few days off next week."