
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 the expansion of $(\sqrt[3]{x} + x^2)^{2n}$, the sum of the coefficients is 992 more than the sum of the binomial coefficients in the expansion of $(3x-1)^n$. Find in the expansion of $(2x- \frac{1}{x})^{2n}$:  
(1) The 10th term  
(2) The constant term;  
(3) The term with the largest absolute value of the coefficient.

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