
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
Let $S_{n}$ be the sum of the first $n$ terms of the sequence ${a_{n}}$, and $S_{n} = 2a_{n} - n + 1$ for all $n \in \mathbb{N}^*$, and $b_{n} = a_{n} + 1$.

1. Find the general term formula for the sequence ${b_{n}}$.
2. Find the sum $T_{n}$ of the first $n$ terms of the sequence ${nb_{n}}$.

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