
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 that the arithmetic sequence $\{a_{n}\}$ has a common difference of $d=2$, and the geometric sequence $\{b_{n}\}$ satisfies $b_{1}=a_{1}$, $b_{2}=a_{4}$, $b_{3}=a_{13}$.

1. Find the general term formula for $\{a_{n}\}$;
2. Find the sum of the first $n$ terms, $S_{n}$, for $\{b_{n}\}$.

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