
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 the arithmetic sequence $\{a_{n}\}$ satisfies $a_{1}=1$, $a_{4}=7$; the sequence $\{b_{n}\}$ satisfies $b_{1}=a_{2}$, $b_{2}=a_{5}$, and the sequence $\{b_{n}-a_{n}\}$ is a geometric sequence.

(I) Find the general term formulas for the sequences $\{a_{n}\}$ and $\{b_{n}\}$;

(II) Find the sum of the first $n$ terms of the sequence $\{b_{n}\}$, denoted as $S_{n}$.

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