
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 $\{a\_n\}$ with the sum of its first $n$ terms denoted as $S\_n$, and $2a\_n = S\_n + 2$ for all $n \in \mathbb{N}^*$.

(1) Find the general formula for the terms of the sequence $\{a\_n\}$.

(2) Let $b\_n = \log\_2(a\_n)$. Find the sum of the first $n$ terms, denoted as $T\_n$, of the sequence $\{\frac{1}{b\_n b\_{n+2}}\}$.

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