
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
Given \( f(x) = 4x^4 - 2x^3 - 16x^2 + 5x + 9 \) and \( g(x) = 2x^3 - x^2 - 5x + 4 \), find \( u(x) \) and \( v(x) \) such that \( u(x)f(x) + v(x)g(x) = \gcd(f(x), g(x)) \).

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