
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 an arithmetic sequence $\{b_{n}\}$ and a geometric sequence $\{a_{n}\}$ with $q \neq 1$, such that $a_{1} = b_{1} = 3$, $a_{2} = b_{4}$, and $a_{3} = b_{13}$.

1. Find the general terms $a_{n}$ and $b_{n}$.
2. Let $c_{n} = a_{n}b_{n}$, find the sum $S_{n}$ of the first $n$ terms of the sequence $\{c_{n}\}$.

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