
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 $\{a_n\}$ with the first term $a_1= \frac{1}{3}$, and it satisfies $a_{n+1}= \frac{1}{3}a_{n}$. Let $b_{n}+2=4\log_{\frac{1}{3}}a_{n}$ $(n\in\mathbb{N}^*)$, and the sequence $\{c_{n}\}$ satisfies $c_{n}=a_{n}\cdot b_{n}$.  
(I) Find the general formula for the sequence $\{b_{n}\}$.  
(II) Find the sum of the first $n$ terms of the sequence $\{c_{n}\}$, $S_{n}$.

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