
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 $p,$ $q,$ and $r$ are zeros of a polynomial $Q(z) = z^3 - 2z^2 + sz + t,$ and $|p|^2 + |q|^2 + |r|^2 = 300.$ The points corresponding to $p,$ $q,$ and $r$ in the complex plane are the vertices of a right triangle with hypotenuse $k.$ Find $k^2.$

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