
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
In the geometric sequence $\{a_n\}$, it is known that $a_1=2$ and $a_4=16$.  
(I) Find the general formula for the sequence $\{a_n\}$.  
(II) If $a_3$ and $a_5$ are respectively the third and fifth terms of the arithmetic sequence $\{b_n\}$, find the general formula for the sequence $\{b_n\}$ and the sum of the first $n$ terms $S_n$.

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