
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 \(PQR\), \(PQ = 15\), \(QR = 16\), and \(PR = 17\), and point \(M\) is the intersection of the medians. Points \(P'\), \(Q'\), and \(R'\), are the images of \(P\), \(Q\), and \(R\), respectively, after a \(180^\circ\) rotation about \(M\). What is the area of the union of the two regions enclosed by the triangles \(PQR\) and \(P'Q'R'\)?

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