
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 expansion of the expression $(\sqrt{x}+\frac{1}{x})^n$, the ratio of the binomial coefficient of the 4th term to that of the 5th term is 1:3.
(1) Find the constant term in the expansion;
(2) Find the term with the maximum binomial coefficient.

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