
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 $\{a\_n\}$ where all terms are positive numbers and satisfy $a\_m \cdot a\_n = 2^{m+n+2}$ for any positive integers $m$ and $n$.
(I) Find the sum of the first $n$ terms, denoted as $S\_n$, of the sequence $\{\log \_2 a\_n\}$.
(II) Let $b\_n = a\_n \cdot \log \_2 a\_n (n \in \mathbb{N}^*)$, find the sum of the first $n$ terms, denoted as $T\_n$, of the sequence $\{b\_n\}$.

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