
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 monic polynomial of degree \( n \) with real coefficients, where the first two terms after \( x^n \) are \( b_{n-1}x^{n-1} \) and \( b_{n-2}x^{n-2} \), and it is given that \( b_{n-1} = -2b_{n-2} \). Find the absolute value of the greatest 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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