
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 finds another piece of Michael's paper. It's another monic polynomial of degree $n$ with real coefficients. The polynomial is described as $x^n + a_{n-1}x^{n-1} + a_{n-2}x^{n-2} + c$, with a note that $a_{n-1} = 2a_{n-2}$. She can't find the precise values of $a_{n-1}$, $a_{n-2}$, or $c$, but is tasked to find the absolute value of the lower bound for the sum of the squares of the roots of this polynomial.

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