
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 $(\frac{1}{2} + 2x)^n$,

(1) If the binomial coefficients of the 5th, 6th, and 7th terms form an arithmetic sequence, find the coefficient of the term with the maximum binomial coefficient in the expansion.

(2) If the sum of the binomial coefficients of the first three terms is 79, find the term with the maximum coefficient in the expansion.

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