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 quadrilateral $A B C D$ the diagonal $B D$ is the bisector of $\angle A B C$ and $A C=B C$. Given $\angle B D C=80^{\circ}$ and $\angle A C B=20^{\circ}, \angle B A D$ is equal to:
<image1>
Choices:
(A) $90^{\circ}$
(B) $100^{\circ}$
(C) $110^{\circ}$
(D) $120^{\circ}$
(E) $135^{\circ}$ 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 quadrilateral $A B C D$ the diagonal $B D$ is the bisector of $\angle A B C$ and $A C=B C$. Given $\angle B D C=80^{\circ}$ and $\angle A C B=20^{\circ}, \angle B A D$ is equal to:
<image1>
Choices:
(A) $90^{\circ}$
(B) $100^{\circ}$
(C) $110^{\circ}$
(D) $120^{\circ}$
(E) $135^{\circ}$ 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