
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
\( p(x) \) is a polynomial of degree less than 1992 such that \( p(0) \), \( p(1) \), \( p(-1) \) are all non-zero. The 1992nd derivative of \( \frac{p(x)}{x^3 - x} \) is \( \frac{f(x)}{g(x)} \) for polynomials \( f(x) \) and \( g(x) \). Find the smallest possible degree of \( f(x) \).

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