
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 points B and D, which are located one-third and two-thirds along two opposite edges not containing A or C, respectively. Calculate the area of quadrilateral ABCD.
A) $\sqrt{3}$
B) $2\sqrt{3}$
C) $\frac{2\sqrt{10}}{3}$
D) $\frac{4\sqrt{3}}{3}$

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