
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 $\left\{a_{n}\right\}$, where $a_{1}=4$ and $na_{n+1}-(n+1)a_{n}=2n^{2}+2n$,

1. Find the general term formula for $\left\{a_{n}\right\}$.
2. Find the sum of the first $n$ terms, $S_{n}$, of the sequence $\left\{\frac{1}{a_{n}}\right\}$.

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