
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
The sequence $\{a\_n\}$ has a sum of its first $n$ terms denoted as $S\_n$, with $a\_1=1$ and $a_{n+1} = 2S\_n + 1$ for $n \geq 1$.
(1) Find the general term formula for $\{a\_n\}$;
(2) Find $S\_n$.

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