
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 $\{a_n\}$, the sum of its first $n$ terms is $S_n$, and it is also given that $2a_5 - S_4 = 2$ and $3a_2 + a_6 = 32$.

(I) Find the general term formula for sequence $\{a_n\}$.
(II) Let $T_n = \frac{a_1}{2} + \frac{a_2}{4} + \ldots + \frac{a_n}{2^n}, n \in \mathbb{N}_+$, find $T_n$.

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