
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, where $XY = 16$, $YZ = 17$ and $ZX = 18$, point O is the centroid. After rotating triangle $XYZ$ by $180^\circ$ around point O, the vertices $X'$, $Y'$, and $Z'$ are formed corresponding to $X$, $Y$, and $Z$, respectively. What is the area of the union of the triangles $XYZ$ and $X'Y'Z'$?

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