
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 $\{a\_n\}$ with its first $n$ terms sum $S\_n$, and it satisfies $S\_n = 2 - a\_n$ for $n = 1, 2, 3, ...$.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. If sequence $\{b\_n\}$ satisfies $b\_1 = 1$ and $b\_{n+1} = b\_n + a\_n$, find the general term formula for the sequence $\{b\_n\}$.

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