
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
In a geometric sequence $\{a_n\}$ where all terms are positive, if $\log_{2}a_{2} + \log_{2}a_{8} = 1$, then $a_{3} \cdot a_{7} =$ ?

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