
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
If the constant term in the expansion of the binomial $\left( \frac{2}{\sqrt[3]{x}} + \sqrt{x} \right)^n$ is the fifth term, find:  
(1) The value of $n$;  
(2) Let the sum of the coefficients in the expansion be $A$, find the value of $\sqrt[10]{A}$;  
(3) The term with the maximum coefficient in the expansion.

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