<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provide the user with the answer. You should try to truely solve the question by yourself without cheating.  <|im_end|>
<|im_start|>user
 Given a geometric sequence {a_n}, where a_3 and a_{15} are the two roots of the equation x^2 - 6x + 1 = 0, find the product a_7a_8a_9a_{10}a_{11}. Express your answer as a single numerical value. Show your work in <think> </think> tags. And return the final answer in <answer> </answer> tags.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user
1
Given a geometric sequence {a_n}, where a_3 and a_{15} are the two roots of the equation x^2 - 6x + 1 = 0, find the product a_7a_8a_9a_{10}a_{11}. Express your answer as a single numerical value.
test