
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 a sequence $\{a\_n\}$ that satisfies $\frac{a\_1}{2} + \frac{a\_2}{2^2} + \frac{a\_3}{2^3} + \dots + \frac{a\_n}{2^n} = n^2 + n$.

1. Find the general formula for the sequence $\{a\_n\}$.
2. If $b\_n = \frac{(-1)^n a\_n}{2}$, 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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