<|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} with a_n > 0, where a_3 and a_7 are the roots of the equation x^2 - 32x + 64 = 0, calculate the value of log_2(a_1) + log_2(a_2) + log_2(a_3) +... + log_2(a_9). Express your answer as a single integer. 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
27
Given a geometric sequence {a_n} with a_n > 0, where a_3 and a_7 are the roots of the equation x^2 - 32x + 64 = 0, calculate the value of log_2(a_1) + log_2(a_2) + log_2(a_3) +... + log_2(a_9). Express your answer as a single integer.
test