
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
Let $\{a_n\}$ be an arithmetic sequence, and $\{b_n\}$ be a geometric sequence with all positive terms, and $a_1=b_1=1$, $a_3+b_5=21$, $a_5+b_3=13$.  
(I) Find the general formula for $\{a_n\}$ and $\{b_n\}$.  
(II) Calculate the sum of the first $n$ terms $S_n$ of the sequence $\left\{ \frac{a_n}{b_n} \right\}$.

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