
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
Find the polynomial \( q(x) \), with real coefficients, such that 
\[ q(x^4) - q(x^4 - 3) = [q(x)]^3 + 18 \] for all real numbers \( x \).

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