
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 $\frac{a\_1}{2}$ + $\frac{a\_2}{2^2}$ + $\frac{a\_3}{2^3}$ + ... + $\frac{a\_n}{2^n}$ = $n^2 + n$.
(I) Find the general formula for the sequence $\{a\_n\}$;
(II) If the sequence $b\_n$ = $\log\_2{a\_n}$, find the sum of the first $n$ terms, $S\_n$, of the sequence $\{b\_n\}$.

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