
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 a sequence $\left\{ a_n \right\}$ whose sum of the first $n$ terms is $S_n$, and it satisfies $S_n = n^2 + n$, where $n \in N^*$,

(1) Find the general formula for $\left\{ a_n \right\}$;

(2) Find the sum of the first $n$ terms of the sequence $\left\{ \frac{1}{(n+1)a_n} \right\}$.

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