
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 ratio of the coefficient of the fifth term to the coefficient of the third term in the expansion of ${{(\sqrt{x}-\frac{2}{{x}^{2}})}^{n}}$ is $10:1$

$(1)$ Find the sum of the coefficients of the expansion; $(2)$ Find the term containing ${{x}^{\frac{3}{2}}}$;

$(3)$ Find the term with the largest coefficient and the term with the largest binomial coefficient in the expansion.

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