
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 $3:4:5$. Segment $XW$ is the angle bisector drawn to the shortest side, dividing it into segments $YW$ and $ZW$. What is the length, in centimeters, of the longer subsegment of side $YZ$ if the length of side $YZ$ is $12$ centimeters?

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