
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
A rectangle $ABCD$ has dimensions $3 \times 2$, where $AB = 3$ and $AD = 2$. Point $E$ is the midpoint of $\overline{AB}$, and point $F$ is the midpoint of $\overline{CD}$. Lines $\overline{AF}$ and $\overline{DE}$ intersect at point $I$. Line $\overline{BD}$ intersects line $\overline{AF}$ at point $H$. Find the area of quadrilateral $BEIH$.

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