
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 sequences ${ a_{n} }$ and ${ b_{n} },$ it is known that $({a}_{1}= \frac{1}{4}, \frac{{a}_{n+1}}{{a}_{n}}= \frac{1}{4},{b}_{n}+2=3{\log }_{ \frac{1}{4}}⁡{a}_{n}(n∈{N}^{∗}).$

1. Find the general terms of the sequences ${ a_{n} }$ and ${ b_{n} }$.
2. Let ${c}_{n}={a}_{n}{⋅}{b}_{n},$ find the sum of the first $n$ terms of the sequence ${c}_{n}$, denoted as ${S}_{n}$.

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