
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 binomial expansion of $\left(\sqrt{x} - \frac{2}{x^2}\right)^n$ ($n \in \mathbb{N}^+$), the ratio of the coefficient of the fifth term to the coefficient of the third term is 10:1.  
(1) Find the sum of the coefficients of all terms in the binomial expansion;  
(2) Find the term with the largest coefficient and the term with the largest binomial coefficient in the binomial expansion.

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