
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
Suppose \(ABC\) is a triangle such that \(AB = 13\), \(BC = 15\), and \(CA = 14\). Say \(D\) is the midpoint of \(\overline{BC}\), \(E\) is the midpoint of \(\overline{AD}\), \(F\) is the midpoint of \(\overline{BE}\), and \(G\) is the midpoint of \(\overline{DF}\). Compute the area of triangle \(EFG\).

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