
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 the fourth-degree polynomial \( f(x) \) with integer coefficients satisfy:
\[ f(1 + \sqrt[3]{3}) = 1 + \sqrt[3]{3} \]
\[ f(1 + \sqrt{3}) = 7 + \sqrt{3} \]
Find \( f(x) = \qquad \)

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