
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
The equation $a^8xy - a^7y - a^6x = a^5(b^5 - 1)$ is equivalent to the equation $(a^mx - a^n)(a^py - a^3) = a^5b^5$ for some integers $m$, $n$, and $p$. Find the product $mnp$.

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