
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
The diagonal $DB$ of rectangle $ABCD$ is divided into three segments of length $2$, $2$, and $4$ by parallel lines $L$ and $L'$ that pass through $A$ and $C$, respectively, and are perpendicular to $DB$. Calculate the area of rectangle $ABCD$.
A) $12\sqrt{2}$
B) $14\sqrt{2}$
C) $16\sqrt{2}$
D) $18\sqrt{2}$
E) $20\sqrt{2}$

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