
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 that the sum of the coefficients of all terms in the expansion of $(\sqrt[3]{x} + x^2)^{2n}$ is greater than the sum of the binomial coefficients in the expansion of $(3x - 1)^n$ by $992$, find:
$(1)$ the $10^{\text{th}}$ term,
$(2)$ the constant term, and
$(3)$ the term with the maximum absolute coefficient value in the expansion of $(2x - \frac{1}{x})^{2n}$.

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