
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 $$(2x+ \frac {3}{ \sqrt[3]{x}})^{n},$$ the ratio of the binomial coefficient of the third term to that of the second term is 5:2.  
(1) Find the value of $n$;  
(2) Find the coefficient of the term containing $x^2$;  
(3) Find the term with the maximum coefficient in the expansion.

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