
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
A monotonically increasing sequence $\{a\_n\}$ has a sum of its first $n$ terms denoted as $S\_n$, and satisfies the equation $4S\_n = a\_n^2 + 4n$.
(1) Find the general term formula for the sequence $\{a\_n\}$;
(2) Sequence $\{b\_n\}$ satisfies $\frac{1}{2}a_{n+1} + \log\_2 b\_n = \log\_2 a\_n$, find the sum of the first $n$ terms of sequence $\{b\_n\}$, denoted as $T\_n$.

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