
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 that the terms in the arithmetic sequence $\{a\_n\}$ are non-zero and satisfy $a\_3 - \frac{a\_7^2}{2} + a\_{11} = 0$, and the sequence $\{b\_n\}$ is a geometric sequence with $b\_7 = a\_7$, calculate $b\_1 \cdot b\_{13}$.

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