
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 complex numbers $\alpha, \beta,$ and $\gamma$ are zeros of a polynomial $Q(z) = z^3 + sz + t$ such that $|\alpha|^2 + |\beta|^2 + |\gamma|^2 = 360$. The points corresponding to $\alpha, \beta,$ and $\gamma$ in the complex plane form an equilateral triangle. Calculate the square of the side length of this triangle.

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