
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
A circle is inscribed in a triangle with side lengths $5, 12$, and $13$. Let the segments of the side of length $5$, made by a point of tangency, be $r$ and $s$, with $r<s$. Determine the ratio $\frac{r}{s}$.

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