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>Find the equivalent torsional spring constant of the system shown in <image 1>. Assume that k1, k2, k3, and k4 are torsional and k5 and k6 are linear spring constants.
A. $k_{et}=(\frac{k_{1}k_{2}k_{3}}{k_{2}k_{3}+k_{1}k_{3}+k_{1}k_{2}})+k_{5}+R^2{(k_{4}+k_{6})}$
B. $k_{et}=(\frac{k_{1}k_{2}k_{3}}{k_{2}k_{3}+k_{1}k_{3}+k_{1}k_{2}})+k_{4}+R^2{(k_{5}+k_{6})}$
C. $k_{et}=(\frac{k_{1}k_{2}k_{3}}{k_{2}k_{3}+k_{1}k_{3}+k_{1}k_{2}})+k_{6}+R^2{(k_{4}+k_{5})}$

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
Find the equivalent torsional spring constant of the system shown in <image 1>. Assume that k1, k2, k3, and k4 are torsional and k5 and k6 are linear spring constants.
A. $k_{et}=(\frac{k_{1}k_{2}k_{3}}{k_{2}k_{3}+k_{1}k_{3}+k_{1}k_{2}})+k_{5}+R^2{(k_{4}+k_{6})}$
B. $k_{et}=(\frac{k_{1}k_{2}k_{3}}{k_{2}k_{3}+k_{1}k_{3}+k_{1}k_{2}})+k_{4}+R^2{(k_{5}+k_{6})}$
C. $k_{et}=(\frac{k_{1}k_{2}k_{3}}{k_{2}k_{3}+k_{1}k_{3}+k_{1}k_{2}})+k_{6}+R^2{(k_{4}+k_{5})}$

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