
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 $ABC$, the sides have lengths in the ratio $3:4:5$. Segment $BE$ is the angle bisector of $\angle B$, where $BE$ bisects the longest side $AC$ into segments $AE$ and $EC$. What is the length, in units, of the shorter subsegment of side $AC$ if the length of $AC$ is $20$ units? Express your answer as a common fraction.

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