
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 sequence $\{a_{n}\}$ satisfies: $a_{1}=1$, $a_{n+1}=2a_{n}$, and the sequence $\{b_{n}\}$ satisfies: $b_{1}=3$, $b_{4}=11$, and $\{a_{n}+b_{n}\}$ is an arithmetic 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 $\{b_{n}\}$.

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