
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
Let rectangle \(ABCD\) have lengths \(AB = 20\) and \(BC = 12\). Extend ray \(BC\) to \(Z\) such that \(CZ = 18\). Let \(E\) be the point in the interior of \(ABCD\) such that the perpendicular distance from \(E\) to \(\overline{AB}\) is 6 and the perpendicular distance from \(E\) to \(\overline{AD}\) is 6. Let line \(EZ\) intersect \(AB\) at \(X\) and \(CD\) at \(Y\). Find the area of quadrilateral \(AXYD\).

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