
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 the sequence $\{ a\_n \}$ that satisfies: $(a\_1+2a\_2+...+na\_n=4-\frac{n+2}{2^{n-1}}, n\in \mathbb{N}^*)$.

(1) Find the general formula for the sequence $\{ a\_n \}$.
(2) If $\{ b\_n = (3n-2)a\_n \}$, find the sum of the first $n$ terms of the sequence $\{ b\_n \}$, denoted as $S\_n$.

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