
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 are $a$ and $b$, and the hypotenuse is $c$. A perpendicular dropped from the right angle vertex divides the hypotenuse $c$ into two segments, $r$ and $s$, adjacent respectively to $a$ and $b$. If the ratio of $a$ to $b$ is 2:5, find the ratio of $r$ to $s$.
A) 1:3
B) 1:9
C) 4:25
D) 3:10
E) 5:18

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