
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
Let the sequence $\{a_n\}$ satisfy $a_1+3a_2+3^2a_3+\ldots+3^{n-1}a_n=\frac{n}{3}$, where $a\in \mathbb{N}^*$.  
(I) Find the general term of the sequence $\{a_n\}$.  

(II) Let $b_n=\frac{n}{a_n}$, find the sum of the first $n$ terms of the sequence $\{b_n\}$, denoted as $S_n$.

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