
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 binomial coefficients in the expansion of $(\sqrt[3]{x} + x^2)^{2n}$ is 992 times larger than the sum of the binomial coefficients in the expansion of $(3x - 1)^n$. Find:

(1) The term with the largest binomial coefficient in the expansion of $\left(\begin{matrix} 2x - \frac{1}{x} \end{matrix}\right)^{2n}$.

(2) The term with the largest absolute value of the coefficient in the expansion of $\left(\begin{matrix} 2x - \frac{1}{x} \end{matrix}\right)^{2n}$.

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