
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 $\{a_n\}$, let $S_n$ denote the sum of the first $n$ terms, with $S_n = \frac{1}{3}(a_n - 1)$ for $n \in \mathbb{N^*}$.  
(1) Determine the values of $a_1$, $a_2$, $a_3$.  
(2) Find the general formula for $a_n$.

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