
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 \( r \) and \( s \) are relatively prime positive integers such that \(\frac{r}{s} = \frac{2(\sqrt{2} + \sqrt{10})}{5(\sqrt{3 + \sqrt{5}})}\), find \( r \) and \( s \).

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