
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 expression $(2x + \frac{1}{\sqrt{x}})^n$ $(n \in \mathbb{N}^*)$, the ratio of the binomial coefficients of the second and third terms in its expansion is $2:5$. Complete the following tasks based on the requirements:  
(I) Find the value of $n$;  
(II) Find the term containing $x^3$ in the expansion.

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