
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 rectangle $ADEH$, points $B$ and $C$ bisect $\overline{AD}$, and points $G$ and $F$ bisect $\overline{HE}$. Further, let $AH = 2$ and $AD = 4$. Determine the area of quadrilateral $WXYZ$ created by the intersection of line segments $AB, BC, HG,$ and $GF$.

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