
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 an arithmetic sequence $\{a_n\}$ with a non-zero common difference, if $2a_3 - a_7^2 + 2a_{11} = 0$, and $\{b_n\}$ is a geometric sequence with $b_7 = a_7$, find the value of $\log_2(b_6 b_8)$.

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