
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
Let $x,$ $y,$ and $z$ be nonzero complex numbers such that $x + y + z = 10$ and
\[
2((x - y)^2 + (x - z)^2 + (y - z)^2) = xyz.
\]
Find $\frac{x^3 + y^3 + z^3}{xyz}$.

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