
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 $a_1 = \frac{1}{4}$, $\frac{a_{n+1}}{a_n} = \frac{1}{4}$, and $b_n + 2 = 3\log_{\frac{1}{4}}a_n$ ($n \in \mathbb{N}^*$).
(1) Find the general formulas for the sequences $\{a_n\}$ and $\{b_n\}$.
(2) Let $c_n = a_n \cdot b_n$, find the sum of the first $n$ terms of the sequence $\{c_n\}$, $S_n$.

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