
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
Suppose that $\{b\_n\}$ is a geometric sequence, and $m$, $n$, $p$ are distinct positive integers. Then, there is a correct conclusion: $(\frac{b\_p}{b\_n})^m \cdot (\frac{b\_m}{b\_p})^n \cdot (\frac{b\_n}{b\_m})^p = 1$. By analogy with this property, if $\{a\_n\}$ is an arithmetic sequence, and $m$, $n$, $p$ are distinct positive integers, then there is a correct conclusion: \_\_\_\_\_\_.

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