
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 relationship between the terms of a geometric sequence is given by $a_n = r^{n-1}a_1$, where $r$ is the common ratio and $a_1$ is the first term. Given that $a_2 \cdot a_6 = 4$, determine the value of $a_4$.

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