
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 with a ratio of the legs being $1:3$, a perpendicular from the vertex of the right angle to the hypotenuse divides the hypotenuse into two segments. Find the ratio of these two segments.
A) $1:3$
B) $1:5$
C) $1:9$
D) $1:7$
E) $1:11$

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