
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
Given an arithmetic sequence $\{a_n\}$ where no term is $0$, and it satisfies $a_5 - a_7^2 + a_9 = 0$, and a geometric sequence $\{b_n\}$ with $b_7 = a_7$, the value of $b_2b_8b_{11}$ is \_\_\_\_\_\_.

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