
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
Morris, while cleaning up after his cat, discovers a torn piece of paper with part of a math problem on it. He sees that there's a monic polynomial of degree $n$ with real coefficients, the first two terms after $x^n$ being $a_{n-1}x^{n-1}$ and $a_{n-2}x^{n-2}$. Curiously, the coefficients meet the condition $a_{n-1}=-2a_{n-2}$. Morris wants to find the sum of the squares of the roots. Although he doesn't know the values of $n$, or $a_{n-1}$, he intuitively seeks to determine the minimum possible value of the sum of the squares of the roots.

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