
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 expression $27x^9 - 512y^9$ can be factored into the form $(ax + by)(cx^3 + dxy^2 + ey^3)(fx + gy)(hx^3 + jxy^2 + ky^3)$. Find the sum of integers $a$, $b$, $c$, $d$, $e$, $f$, $g$, $h$, $j$, and $k$.

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