
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
Consider a cubic monic polynomial $p(x) = x^3 + a_2x^2 + a_1x + a_0$ with real coefficients. It is known that $a_1 = -2a_2$. Find the minimum value of the sum of squares of the roots of the polynomial $p(x)$.

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