
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
Let $ABCD$ be a $3 \times 3$ square with vertices at $A(0, 3)$, $B(0, 0)$, $C(3, 0)$, and $D(3, 3)$. Point $E$ is located at $\frac{2}{3}$ the distance from $A$ to $B$ and point $F$ is at $\frac{2}{3}$ the distance from $B$ to $C$. If $\overline{AF}$ and $\overline{DE}$ intersect at point $I$ and $\overline{BD}$ and $\overline{AF}$ intersect at point $H$, find the area of quadrilateral $BEIH$.

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