
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
Find the area of quadrilateral \(ABCD\) given that \(\angle ABC = \angle ACD = 90^\circ\), \(AC = 20\), \(CD = 30\), and the diagonals \(AC\) and \(BD\) intersect at point \(E\) with \(AE = 5\).

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