
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 $ABC,$ $AB = 25,$ $BC = 39,$ $AC = 42,$ and point $G$ is the intersection of the medians. Points $A',$ $B',$ and $C',$ are the images of $A,$ $B,$ and $C,$ respectively, after scaling down by a factor of $\frac{1}{2}$ about $G.$ What is the area of the union of the regions enclosed by the triangles $ABC$ and $A'B'C'$?

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