
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
It is known that the sequence $\{b_n\}$ is a geometric sequence, $b_{n} = 2^{a_{n}-1}$, where $a_{1} = 1$, $a_{3} = 3$, and $c_{n} = a_{n} \cdot b_{n}$. Find the sum of the first $n$ terms of the sequence $\{c_{n}\}$, denoted as $S_{n}$.

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