
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 triangle $XYZ$, the sides are in the ratio of $3:4:5$. Segment $XE$ is the angle bisector of $\angle X$, drawn to the longest side, dividing it into segments $YE$ and $ZE$. What is the length, in units, of the shorter subsegment of the longest side if the length of the longest side is $15$ units? Express your answer as a common fraction.

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