
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 an arithmetic sequence $\{a_n\}$ with the first three terms being $a-1, 4, 2a$, denote the sum of the first $n$ terms as $S_n$.

(I) Find the value of the real number $a$ and the general term formula $(a_n)$;

(II) Let $b_n = \frac{S_n}{n}$, find the sum of the first $n$ terms $(T_n)$ of the sequence $\{2^{b_n}\}$.

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