
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
Let \( x_{1} \) and \( x_{2} \) be the largest roots of the polynomials \( f(x) = 1 - x - 4x^{2} + x^{4} \) and \( g(x) = 16 - 8x - 16x^{2} + x^{4} \), respectively. Find \( \frac{x_{1}}{x_{2}} \).

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