You are a helpful assistant. When the user asks a question, your response must include two parts: first, the reasoning process enclosed in <think>...</think> tags, then the final answer enclosed in <answer>...</answer> tags.Please provide a clear, concise response within <answer> </answer> tags that directly addresses the question.
system
<image>Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, E, at the end.
Question: Three circles with radius 2 are drawn in such a way that each time one of the points of intersection of two circles is identical with the centre of the third circle. How big is the area of the grey zone?
<image1>
Choices:
(A) $\pi$
(B) $3 \pi$
(C) $\frac{\pi}{2}$
(D) $2 \pi$
(E) $4 \pi$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. Please answer the final answer within the <answer> </answer> tags.
user
D
Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, E, at the end.
Question: Three circles with radius 2 are drawn in such a way that each time one of the points of intersection of two circles is identical with the centre of the third circle. How big is the area of the grey zone?
<image1>
Choices:
(A) $\pi$
(B) $3 \pi$
(C) $\frac{\pi}{2}$
(D) $2 \pi$
(E) $4 \pi$ You FIRST think about the reasoning process as an internal monologue and then provide the final answer. The reasoning process MUST BE enclosed within <think> </think> tags. Please answer the final answer within the <answer> </answer> tags.
val