
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
In a right triangle, the lengths of the legs a and b maintain a ratio of 3 : 4, and the hypotenuse is c. A perpendicular is dropped from the vertex of the right angle to the hypotenuse, dividing it into two segments: r adjacent to a and s adjacent to b. Find the ratio of r to s.

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