
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 expansion of $\left( \sqrt{x} - \frac{2}{x^2} \right)^n$ (where $n \in \mathbb{N}^*$) has its fifth term's coefficient to the third term's coefficient ratio as 10:1.  
(1) Find the value of $n$ and the term with the maximum binomial coefficient in the expansion;  
(2) Find the term containing $x^{\frac{3}{2}}$ in the expansion and the sum of the coefficients of all terms in the expansion.

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