
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
If $\{b_n\}$ is a geometric sequence, and $m$, $n$, $p$ are distinct positive integers, then the correct conclusion is: $\left( \frac{b_p}{b_n}\right)^m \cdot \left( \frac{b_m}{b_p}\right)^n \cdot \left( \frac{b_n}{b_m}\right)^p = 1$. By analogy with the above property, correspondingly, if $\{a_n\}$ is an arithmetic sequence, and $m$, $n$, $p$ are distinct positive integers, then the correct conclusion is:

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