
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 sequence $\{a_{n}\}$ satisfies $a_{1}=1$, $na_{n+1}=(n+1)a_{n}+n(n+1)$, where $n\in\mathbb N^{*}$.
(1) Find the general term formula of the sequence $\{a_{n}\}$;
(2) Let $b_{n}=3^{n}\cdot\sqrt{a_{n}}$, find the sum of the first $n$ terms $S_{n}$ of the sequence $\{b_{n}\}$.

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