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 diagram, $A B$ has length $1 ; \angle A B C=\angle A C D=90^{\circ}$; $\angle C A B=\angle D A C=\theta$. What is the length of $A D$?
<image1>
Choices:
(A) $\cos \beta+\tg \beta$
(B) $\frac{1}{\cos (2 \beta)}$
(C) $\cos ^{2} \beta$
(D) $\cos (2 \beta)$
(E) $\frac{1}{\cos ^{2} \beta}$ 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 diagram, $A B$ has length $1 ; \angle A B C=\angle A C D=90^{\circ}$; $\angle C A B=\angle D A C=\theta$. What is the length of $A D$?
<image1>
Choices:
(A) $\cos \beta+\tg \beta$
(B) $\frac{1}{\cos (2 \beta)}$
(C) $\cos ^{2} \beta$
(D) $\cos (2 \beta)$
(E) $\frac{1}{\cos ^{2} \beta}$ 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