
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 sum of its first $n$ terms being $S\_n$, if $S\_2 = 16$ and $a\_1$, $a\_2 - 4$, $a\_3 - 8$ form a geometric sequence:

(I) Find the general term formula $a\_n$ for the sequence $\{a\_n\}$;

(II) Let $b\_n = \frac{S\_n}{2n} \left(\frac{a\_n - 2}{2n}\right)^n$, find the sum of the first $n$ terms, $T\_n$, for the sequence $\{b\_n\}$.

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