
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 \(a^{8}xyz - a^{7}yz - a^{6}xz = a^{5}(c^{5} - 1)\) is equivalent to the equation \((a^{m}xz - a^{n})(a^{p}yz - a^{3}) = a^{5}c^{5}\) for some integers \(m\), \(n\), and \(p\). Find the product \(mnp\).

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