
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 $\{a_n\}$. Given that $a_n > 0$ and $4S_n = (a_n + 3)(a_n - 1)$ for $n \in \mathbb{N}^*$. Find the general formula for $a_n$, which is $a_n =$ ______.

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