
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 the positive arithmetic sequence {a<sub>n</sub>} with common ratio q, a<sub>4</sub> = 4. Find the minimum value of log<sub>2</sub>q when 2a<sub>2</sub> + a<sub>6</sub> is minimized.

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