
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 \(ABCD\) be a quadrilateral with \(\angle BAD = \angle ABC = 90^\circ\), and suppose \(AB = BC = 1\), \(AD = 2\). The circumcircle of \(ABC\) meets \(\overline{AD}\) and \(\overline{BD}\) at points \(E\) and \(F\), respectively. If lines \(AF\) and \(CD\) meet at \(K\), compute \(EK\).

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