
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 $b$, with the hypotenuse being $c$. A perpendicular from the right angle vertex divides the hypotenuse $c$ into two segments $r$ and $s$, where $r$ is adjacent to $a$ and $s$ is adjacent to $b$. Given that the ratio of $a$ to $b$ is $2 : 5$, find the ratio of $r$ to $s$.

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