
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
Two right triangles have hypotenuses of lengths $h_1$ and $h_2$ respectively, and the radii of their inscribed circles are $r_1$ and $r_2$ respectively. If $(r/s)_1$ denotes the ratio of the radius of the inscribed circle to the semiperimeter for the first triangle, and $(r/s)_2$ for the second, find the ratio $(r/s)_1/(r/s)_2$ in terms of $h_1$, $h_2$, $r_1$, and $r_2$.

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