
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 diagram, the circle has radius \(\sqrt{5}\). Rectangle \(ABCD\) has \(C\) and \(D\) on the circle, \(A\) and \(B\) outside the circle, and \(AB\) tangent to the circle. What is the area of \(ABCD\) if \(AB = 4AD\)?

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