
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
Suppose that \( f(x) = x^4 - x^3 - 1 \) and \( g(x) = x^8 - x^6 - 2x^4 + 1 \). If \( g(x) = f(x) h(x) \), determine the polynomial function \( h(x) \).

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