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: In the accompanying figure, segments $AB$ and $CD$ are parallel, the measure of angle $D$ is twice the measure of angle $B$, and the measures of segments $AB$ and $CD$ are $a$ and $b$ respectively.
<image1>
Then the measure of $AB$ is equal to
Choices:
(A) $\frac{1}{2}a+2b$
(B) $\frac{3}{2}b+\frac{3}{4}a$
(C) $2a-b$
(D) $4b-\frac{1}{2}a$
(E) $a+b$ 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
E
Hint: Please answer the question and provide the correct option letter, e.g., A, B, C, D, E, at the end.
Question: In the accompanying figure, segments $AB$ and $CD$ are parallel, the measure of angle $D$ is twice the measure of angle $B$, and the measures of segments $AB$ and $CD$ are $a$ and $b$ respectively.
<image1>
Then the measure of $AB$ is equal to
Choices:
(A) $\frac{1}{2}a+2b$
(B) $\frac{3}{2}b+\frac{3}{4}a$
(C) $2a-b$
(D) $4b-\frac{1}{2}a$
(E) $a+b$ 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