
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 \( P(z) = z^3 + sz + t, \) and \( |p|^2 + |q|^2 + |r|^2 = 350. \) The points corresponding to \( p, \) \( q, \) and \( r \) in the complex plane form a right triangle with hypotenuse \( k. \) Find \( k^2. \)

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