
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 arithmetic sequence $\{a_{n}\}$ with a non-zero common difference, $2a_{5}-a_{7}^{2}+2a_{9}=0$. The sequence $\{b_{n}\}$ is a geometric sequence with $b_{7}=a_{7}$. Calculate the value of $\log_{2}(b_{5}b_{9})$.

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