
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 $a^8xy - a^7y - a^6x = a^5(c^5 - 1)$ is equivalent to the equation $(a^ux - a^v)(a^wy - a^3) = a^5c^5$ for some integers $u$, $v$, and $w$. Find the product $uvw$.

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