
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 $(1+2 \sqrt {x})^{n}$, the coefficient of a certain term is twice that of its preceding term and $\frac {5}{6}$ of its following term.  
(1) Find the term with the maximum binomial coefficient in the expansion;  
(2) Find the term with the maximum coefficient in the expansion.

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