
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 legs are $a$ and $b$, and the hypotenuse is $c$. A perpendicular from the vertex of the right angle divides $c$ into segments $r$ and $s$, adjacent to $a$ and $b$, respectively. If $a : b = 2 : 5$, find the ratio of $r$ to $s$.
**A)** $\frac{1}{4}$  
**B)** $\frac{4}{29}$  
**C)** $\frac{4}{25}$  
**D)** $\frac{1}{5}$  
**E)** $\frac{5}{4}$

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