
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
In the sequence $\left\{a_{n}\right\}$, it is known that $(a_{1}= \frac{1}{4}, \frac{a_{n+1}}{a_{n}}= \frac{1}{4}, b_{n}+2=3\log_{\frac{1}{4}}{a_{n}}\left(n∈\mathbb{N}^{*}\right)$.

(I) Find the general term formula of the sequence $\left\{b_{n}\right\}$;

(II) Suppose the sequence $\left\{c_{n}\right\}$ satisfies ${c_{n}={a_{n}⋅{b_{n}}}}$, find the sum of the first $n$ terms of the sequence $\left\{c_{n}\right\}$ (${S_{n}}$).

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