
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
Square $ABCD$ is inscribed in a circle. Right-angled trapezoid $EFGH$ has vertices $E, F$ on $\overline{CD}$ (with $E$ and $F$ not necessarily at midpoints or vertices of $CD$), vertices $G$ and $H$ on the circle, and $\angle EGH$ right. If the area of square $ABCD$ is $16$, find the area of trapezoid $EFGH$.

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