
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 the sequence $\{a\_n\}$ that satisfies: $(n+1)a_{n-1} = na\_n$ ($n \in \mathbb{N}^*, n \geq 2$), and $a\_3 = 2$.

1. Find the general term formula for the sequence $\{a\_n\}$.
2. Find the sum $S\_n$ of the first $n$ terms of the sequence $\{ \frac{1}{a\_n a\_{n+1}} \}$.

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