
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 $(\sqrt[3]{x} +x^{2})^{2n}$, the sum of the binomial coefficients of its expansion is greater than the sum of the binomial coefficients of the expansion of $(3x-1)^{n}$ by $992$. Find the term with the largest absolute value of the coefficient in the expansion of ${(2x- \frac{1}{x})}^{2n}$.

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