
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
Consider an arithmetic sequence $\{a\_n\}$ with the sum of its first $n$ terms denoted as $S\_n$. Given that $2a\_5 - S\_4 = 2$ and $3a\_2 + a\_6 = 32$,
(I) find the general term formula for the sequence;
(II) let $T\_n = \frac{a\_1}{2} + \frac{a\_2}{4} + \dots + \frac{a\_n}{2^n}, n \in \mathbb{N}^+$, find $T\_n$.

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