
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 \(a,\) \(b,\) and \(c\) be nonzero complex numbers such that \(a + b + c = 30\) and
\[(a - b)^2 + (a - c)^2 + (b - c)^2 = 2abc.\] Find \(\frac{a^3 + b^3 + c^3}{abc}\).

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