
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
If $ABCD$ is a $3 \times 2$ rectangle, with $A(0,0)$, $B(0,2)$, $C(3,2)$, and $D(3,0)$. Let $E$ be the midpoint of $\overline{AB}$, $F$ the midpoint of $\overline{BC}$, $\overline{AF}$ and $\overline{DE}$ intersect at $I$, and $\overline{BD}$ and $\overline{AF}$ intersect at $H$. Calculate the area of quadrilateral $BEIH$.

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