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>Determine the vertical displacements at A of the pin-connected  structure in Figure P9.31. Given: E = 200 GPa,  AAB = 1000 mm2 , and AAC = AAD = 500 mm2 . <image 1>
A. 4.32 mm
B. 4.12 mm
C. 4.22 mm

Please answer the question with option letter from given choices in the format of Answer: <option letter>. 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
B
Determine the vertical displacements at A of the pin-connected  structure in Figure P9.31. Given: E = 200 GPa,  AAB = 1000 mm2 , and AAC = AAD = 500 mm2 . <image 1>
A. 4.32 mm
B. 4.12 mm
C. 4.22 mm

Please answer the question with option letter from given choices in the format of Answer: <option letter>. 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