
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
A cube with side length $2$ is sliced by a plane that passes through two diagonally opposite vertices $A$ and $C$ and the midpoints $B$ and $D$ of two opposite edges not containing $A$ or $C$. What is the area of quadrilateral $ABCD$?
A) $2$
B) $\sqrt{12}$
C) $4\sqrt{2}$
D) $2\sqrt{6}$
E) $\sqrt{24}$

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