
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 \(x, y, z\) be nonzero complex numbers such that \(x + y + z = 18\) and
\[(x - y)^2 + (x - z)^2 + (y - z)^2 = 2xyz.\]
Find \(\frac{x^3 + y^3 + z^3}{xyz}\).

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