
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 around the right angle are \( a \) and \( b \), and the hypotenuse is \( c \). A perpendicular from the right angle vertex divides \( c \) into segments \( r \) and \( s \), adjacent respectively to \( a \) and \( b \). If the ratio of \( a \) to \( b \) is \( 2 : 5 \), then find the ratio of \( r \) to \( s \).

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