
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 a right triangle with legs $a$ and $b$, and hypotenuse $c$, where the ratio $a:b = 2:5$. A perpendicular is dropped from the right angle vertex to the hypotenuse, dividing it into segments $r$ adjacent to $a$ and $s$ adjacent to $b$. Determine the ratio of $r$ to $s$.
A) $\frac{1}{9}$  
B) $\frac{4}{25}$  
C) $\frac{2}{5}$  
D) $\frac{5}{2}$  
E) $\frac{1}{5}$

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