
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
In the geometric sequence $\{a\_n\}$, $a\_n > 0 (n \in \mathbb{N}^*)$, and $a\_1a\_3 = 4$, $a\_3 + 1$ is the middle term of the arithmetic sequence formed by $a\_2$ and $a\_4$.
(I) Find the general term formula of the sequence $\{a\_n\}$;
(II) If the sequence $\{b\_n\}$ satisfies $b\_n = a\_{n+1} + \log\_2 a\_n (n = 1, 2, 3...)$, 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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