
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 $P(z) = z^3 + pz^2 + qz + r$. It is given that $|a|^2 + |b|^2 + |c|^2 = 300$. The points corresponding to $a,$ $b,$ and $c$ in the complex plane are the vertices of a right triangle, with the hypotenuse $h$. Find $h^2.$

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