
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
Given a sequence $\{a_n\}$ which is a geometric sequence with the first term $\frac{1}{4}$ and common ratio $\frac{1}{4}$, let $b_n+2=3\log_{\frac{1}{4}}a_n$ ($n\in\mathbb{N}^*$), and a sequence $\{c_n\}$ satisfies $c_n=a_nb_n$  
(1) Find the general formula for sequences $\{a_n\}$ and $\{b_n\}$.  
(2) Find the sum of the first $n$ terms of sequence $\{c_n\}$, $S_n$.

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