
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 that the sum of the first $n$ terms of the sequence $\{a\_n\}$ is $S\_n$, and it satisfies $S\_n = n^2 + n$, where $n \in \mathbb{N}^*$.

(1) Find the general term formula for $\{a\_n\}$;

(2) Find the sum of the first $n$ terms of the sequence $\{\frac{1}{(n+1)a\_n}\}$.

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