
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 $XYZ$, $XY = 7$, $YZ = 24$, $ZX = 25$, and point $M$ is the intersection of the medians. Points $X'$, $Y'$, and $Z'$ are the images of $X$, $Y$, and $Z$, respectively, after a $180^\circ$ rotation about $M$. What is the area of the union of the two regions enclosed by the triangles $XYZ$ and $X'Y'Z'$?

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