
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 denoted as $S\_n$, and $S\_n^2 - (a\_n + 2)S\_n + 1 = 0 \quad (n \in \mathbb{N}^*)$. Find $a\_1$, $a\_2$ and the general formula for $\{a\_n\}$.

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