
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
Determine the product $mnp$ for integers $m$, $n$, and $p$ such that the equation $b^8xz - b^7z - b^6x = b^5(c^5 - 1)$ is equivalent to the equation $(b^mx-b^n)(b^pz-b^3)=b^5c^5$.

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