
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 the coefficients of the first three terms in the expansion of $(x+ \frac{1}{2})^n$ form an arithmetic sequence, let $(x+ \frac{1}{2})^n = a_0 + a_1x + a_2x^2 + \ldots + a_nx^n$.

(1) Find the value of $a_0$.

(2) Find the largest binomial coefficient.

(3) Find the term with the largest coefficient.

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