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 figure below, choose point $D$ on $\overline{BC}$ so that $\triangle ACD$ and $\triangle ABD$ have equal perimeters. What is the area of $\triangle ABD$?
<image1>
Choices:
(A) $\frac{3}{4}$
(B) $\frac{3}{2}$
(C) $2$
(D) $\frac{12}{5}$
(E) $\frac{5}{2}$ 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: In the figure below, choose point $D$ on $\overline{BC}$ so that $\triangle ACD$ and $\triangle ABD$ have equal perimeters. What is the area of $\triangle ABD$?
<image1>
Choices:
(A) $\frac{3}{4}$
(B) $\frac{3}{2}$
(C) $2$
(D) $\frac{12}{5}$
(E) $\frac{5}{2}$ 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