
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
$G$ and $H$ are midpoints of two adjacent edges of a cube. A trapezium-shaped cross-section is formed cutting through $G$, $H$, and two further vertices, as shown. The edge length of the cube is $2 \sqrt{2}$. What is the area of the trapezium?

A) 9

B) 8

C) $4 \sqrt{5}$

D) $4 \sqrt{3}$

E) $4 \sqrt{2}$

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