
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]


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Given a sequence $\{a_{n}\}$ with the first term $a_{1}=1$, and it satisfies $(a_{n+1}-1)a_{n}+a_{n+1}=0 (n \in \mathbb{N}^{*})$.

(1) Find the general term formula for the sequence $\{a_{n}\}$;

(2) Let $c_{n}=\frac{3^{n}}{a_{n}}$, find the sum of the first $n$ terms, denoted as $S_{n}$, for the sequence $\{c_{n}\}$.

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