
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 adjacent to the right angle are $a$ and $b$, and the hypotenuse is $c$. A perpendicular from the vertex with the right angle divides $c$ into segments $r$ and $s$, adjacent respectively to $a$ and $b$. If $a:b = 2:5$, find the ratio of $r$ to $s$.
A) $2:5$
B) $4:25$
C) $1:2$
D) $8:25$
E) $5:29$

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