
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
In the sequence $\{a_n\}$, $a_1 = 2$, and $3(a_1 + a_2 + \ldots + a_n) = (n + 2)a_n$ for $n \in \mathbb{N}^*$. Find the general formula for $a_n$.

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