
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
Quadrilateral $ABCD$ is a rhombus with a side length of $6 \, \text{cm}$ and a height of $4 \, \text{cm}$. Point $E$ is the midpoint of side $AD$, point $G$ is the midpoint of side $BC$, point $F$ is the intersection of segments $AG$ and $BE$, and point $H$ is the intersection of segments $CE$ and $DG$.

Determine the area of quadrilateral $EFGH$.

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