
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 $\{a\_n\}$, with $a\_1=2$, and the point $(\frac{1}{2}a\_n, a_{n+1}+1)$ lies on the graph of the function $f(x) = 2x + 3$.
(1) Find the general term formula of the sequence $\{a\_n\}$;
(2) If the sequence $b\_n = 2^{a\_n}$, find the sum of the first $n$ terms of the sequence $\{b\_n\}$, denoted as $T\_n$.

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