
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 sum of the binomial coefficients of the second and third terms in the expansion of $\left(\sqrt{x}-\dfrac{2}{x^{2}}\right)^{n}$ is $36$, where $n$ is a positive integer, find:

$\left(I\right)$ the value of $n$;

$\left(II\right)$ the term containing $x^{\frac{3}{2}}$ in the expansion and the term with the largest binomial coefficient.

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