
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 the right trapezoid $A B C D$, the base $A B$ is 1.5 times longer than the diagonal $A C$. The angles $B A D$ and $A D C$ are right angles. The angle $D C A$ is equal to the angle $B C A$. The leg $A D$ is equal to 4. Find the area of the trapezoid $A B C D$.

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