
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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Consider the sequence ${{a_n}}$ that satisfies ${a_1 + \frac{a_2}{3} + \frac{a_3}{3^2} + \cdots + \frac{a_n}{3^{n-1}} = n}$, and ${b_n = n \log_3 a_{4n+1}}$, where $n \in \mathbb{N}^*$.

(I) Find the general term of the sequences ${{a_n}}$ and ${{b_n}}$.

(II) Let ${c_n = \frac{1}{b_n - 1}}$, find the sum of the first $n$ terms, denoted as $S_n$, of the sequence ${{c_n}}$.

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