
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
The perpendicular bisectors of the sides of triangle $XYZ$ intersect its circumcircle at points $X',$ $Y',$ and $Z',$ respectively. If triangle $XYZ$ has a perimeter of 24 and the radius of the circumcircle is 5, determine the total length of the arcs $XX',$ $YY',$ and $ZZ',$ which are opposite to the vertices $X,$ $Y,$ and $Z$ in the circumcircle.

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