
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 sequence $\{a_n\}$ is an arithmetic sequence, $a_1=2$, and $a_2$, $a_4$, $a_8$ form a geometric sequence.  
(I) Find the general formula for the arithmetic sequence $\{a_n\}$.  
(II) If the sequence $\{b_n\}$ is a geometric sequence, and $b_1=a_2$, $b_2=a_4$, find the sum of the first $n$ terms $S_n$ of $\{b_n\}$.

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