
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 the square $ABCD$, points $F$ and $E$ are the midpoints of sides $AB$ and $CD$, respectively. Point $E$ is connected to vertices $A$ and $B$, and point $F$ is connected to vertices $C$ and $D$, as shown in the illustration. Determine the area of the rhombus $FGEH$ formed in the center if the side of the square $AB = 4$.

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