
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 $a^8xy - a^7x - a^6y = a^5(c^5 - 2)$ must be equivalent to $(a^sx - a^t)(a^uy - a^3) = a^5c^5$ for certain integers $s$, $t$, and $u$. Find the product $stu$.

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