
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 general term formula of the sequence $\{a\_n\}$ is $a\_n = \frac{1}{n(n+1)} (n \in \mathbb{N}^*)$, and the sum of the first $n$ terms of the sequence $\{a\_n\}$ is $S\_n$. Find $\lim\limits_{n \to \infty} S\_n =\_\_\_\_\_\_\_\_\_\_\_\_\_.$

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