
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 $\{a\_n\}$, it is known that $a\_1= \frac {1}{4}$, $\frac {a_{n+1}}{a_{n}}= \frac {1}{4}$, and $b\_n+2=3\log _{ \frac {1}{4}}a\_n (n\in\mathbb{N}^*).$
(1) Find the general term formulas for the sequences $\{a\_n\}$ and $\{b\_n\}$;
(2) Let the sequence $\{c\_n\}$ satisfy $c\_n=a\_n\cdot b\_n$, find the sum of the first $n$ terms of $\{c\_n\}$, denoted as $S\_n$.

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