
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 ${a_n}$ where $a_1=1$, $a_3=5$.
1. Find the general term formula for the sequence ${a_n}$.
2. If a geometric sequence ${b_n}$ satisfies $b_1=a_2$, $b_2=a_1+a_2+a_3$, find the sum of the first $n$ terms, $S_n$, for the sequence ${b_n}$.

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