
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
The geometric sequence $\{a_n\}$ satisfies $a_n > 0$ and $a_2a_8=4$. Find the value of $\log_2a_1+\log_2a_2+\log_2a_3+\cdots+\log_2a_9$.

Present the answer in LaTex format: \boxed{Your answer}
user