
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 that the sum of the first $n$ terms of the positive sequence $\{a\_n\}$ is $S\_n$ and satisfies the equation $4S\_n = (a\_n - 1)(a\_n + 3)$, where $n \in \mathbb{N}^*$:

1. Find $a\_n$;
2. If $b\_n = 2^n \cdot a\_n$, 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}
user