
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 \( b \), with the hypotenuse being \( c \). The ratio of sides \( a : b \) is \( 2 : 5 \). A perpendicular from the vertex of the right angle to the hypotenuse divides it into segments \( r \) and \( s \), where \( r \) is adjacent to \( a \) and \( s \) is adjacent to \( b \). Find the ratio \( r : s \).
A) \( 1 : 2 \)
B) \( 4 : 25 \)
C) \( 2 : 5 \)
D) \( 5 : 4 \)
E) \( 10 : 25 \)

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