
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
In rectangle $ABCD$, diagonal $DB$ is divided into three segments of lengths $1$, $2$, and $3$ by parallel lines $L$ and $L'$, which pass through vertices $A$ and $C$ and are perpendicular to diagonal $DB$. Calculate the area of rectangle $ABCD$.
A) $6\sqrt{5}$
B) $12$
C) $12\sqrt{5}$
D) $30$
E) $18\sqrt{3}$

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