
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
Complex numbers \(a\), \(b\), and \(c\) are zeros of a polynomial \(P(z) = z^3 + pz + q\), and \(|a|^2 + |b|^2 + |c|^2 = 360\). The points corresponding to \(a\), \(b\), and \(c\) in the complex plane are the vertices of a right triangle with the right angle at \(a\). Find \(h^2\), where \(h\) is the length of the hypotenuse.

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