
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 $\{a\_n\}$, its sum of the first $n$ terms is $S\_n$. For all $n \in \mathbb{N}^*$, $S\_n = (n + 1)a\_n - n(n + 1)$.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. Let $b\_n = 2^{n - 1}a\_n$, find the sum of the first $n$ terms, $T\_n$, for the sequence $\{b\_n\}$.

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