
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
Wendy continues her math exploration and finds another torn piece of Michael's papers. On this piece, there is another monic polynomial of degree $n$, again with real coefficients. The first two terms following $x^n$ are $a_{n-1}x^{n-1}$ and $a_{n-2}x^{n-2}$. Wendy notes that on this piece, $a_{n-1} = 2a_{n-2}$. Wendy aims to determine the sum of the squares of the roots of this polynomial knowing that neither the degree $n$ nor the coefficients $a_{n-1}$ and $a_{n-2}$ are directly specified, yet she's interested in finding a [greatest] lower bound for the sum of the squares of the roots. She wants to find the absolute value of this lower bound.

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