
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 that $n$ is a positive integer, in the expansion of the binomial $\left(\frac{1}{2} + 2x\right)^n$, if the sum of the binomial coefficients of the first three terms equals 79.  
(1) Find the value of $n$;  
(2) Determine which term in the expansion has the largest coefficient?

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