
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 the zeros of the polynomial \( P(z) = z^3 + sz + t, \) where \( |a|^2 + |b|^2 + |c|^2 = 350. \) In the complex plane, the points corresponding to \( a, \) \( b, \) and \( c \) form a right triangle. If \( a \) and \( b \) are the vertices of the right angle, find the square of the length of the hypotenuse.

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