
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 $\triangle ABC$, $AD$ is an angle bisector of $\angle BAC$ intersecting $BC$ at $D$, and $BE$ is an angle bisector of $\angle ABC$ intersecting $AC$ at $E$. Let $I$ be the incenter of $\triangle ABC$. The midpoint of $AC$ is $F$. Suppose $\triangle ABC$ is isosceles with $AB = AC$. Calculate the area of $\triangle EIF$ as a fraction of the area of $\triangle ABC$.
A) $\frac{1}{6}\qquad$ B) $\frac{1}{8}\qquad$ C) $\frac{1}{9}\qquad$ D) $\frac{1}{12}\qquad$ E) $\frac{1}{16}$

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