
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 $Q(z) = z^4 - 2z^3 + sz + t,$ where $s, t \in \mathbb{C}$. It is given that $|p|^2 + |q|^2 + |r|^2 = 300$. The points corresponding to $p$, $q$, and $r$ in the complex plane form an equilateral triangle. Find the square of the side length of this triangle, denoted as $s^2$.

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