
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 an arithmetic sequence $\{a_n\}$ where $a_2=2$ and $a_4=4$, and a geometric sequence $\{b_n\}$ with positive terms where $b_1=1$ and $b_1+b_2+b_3=7$.  
(1) Find the general formula for sequences $\{a_n\}$ and $\{b_n\}$.  
(2) If $c_n= \frac{a_n}{b_n}$, find the sum of the first $n$ terms of sequence $\{c_n\}$, denoted as $S_n$.

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