
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 sides other than the hypotenuse are $a$ and $b$, with $a:b = 2:5$. If the hypotenuse is $c$, and a perpendicular from the right angle vertex to $c$ is drawn, dividing it into segments $r$ and $s$, adjacent respectively to $a$ and $b$, find the ratio of $r$ to $s$.

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