
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
(1) Let $A$ be the sum of all coefficients and $B$ be the sum of all binomial coefficients in the expansion of $(3x^{\frac{1}{3}}+1)^{n}$. If $A+B=272$, find the coefficient of the $x$ term in the expansion.
(2) If the sum of the first three binomial coefficients in the expansion of $(\frac{1}{2}+2x)^{n}$ 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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