
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
A right triangle has legs with a ratio of $3:4$. When a perpendicular is drawn from the right angle vertex to the hypotenuse, find the ratio of the lengths of the segments of the hypotenuse created by this perpendicular line.

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