
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 $a^8xy - a^7y - a^6x = a^5(b^5 - 2)$ needs to be rewritten in the form $(a^{m'}x - a^{n'})(a^{p'}y - a^{3}) = a^5b^5$ for some integers $m'$, $n'$, and $p'$. Find the product $m'n'p'$.

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