
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 $\{a_n\}$ is an arithmetic sequence, and $a_1=3, a_4=12$, the sequence $\{b_n\}$ satisfies $b_1=4, b_4=20$, and $\{b_n-a_n\}$ is a geometric sequence.  
(I) Find the general formula for sequences $\{a_n\}$ and $\{b_n\}$.  
(II) Find the sum of the first $n$ terms of sequence $\{b_n\}$, denoted as $S_n$.

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