
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 a geometric sequence $\{a_n\}$, it is known that $a_1=3$ and the common ratio $q \neq 1$. There is an arithmetic sequence $\{b_n\}$ such that $b_1=a_1$, $b_4=a_2$, and $b_{13}=a_3$.  
(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 $\{c_n\}$, denoted as $S_n$.

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