
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 \(ABC\), \(AB = 6\), \(BC = 7\), and \(CA = 8\). Let \(D\), \(E\), and \(F\) be the midpoints of sides \(BC\), \(AC\), and \(AB\), respectively. Also, let \(O_A\), \(O_B\), and \(O_C\) be the circumcenters of triangles \(AFD\), \(BDE\), and \(CEF\), respectively. Find the area of triangle \(O_A O_B O_C\).

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