
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
The sides of a right triangle are $a$, $b$, and the hypotenuse is $c$. A perpendicular from the vertex divides $c$ into segments $r$ and $s$, adjacent respectively to $a$ and $b$. If $a : b = 2 : 3$, find the ratio of $r$ to $s$.
- **A)** \(1 : 3\)
- **B)** \(2 : 3\)
- **C)** \(4 : 9\)
- **D)** \(3 : 4\)
- **E)** \(1 : 2\)

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