
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  $ ABC$  be a triangle with  $ AB \equal{} AC$  . The angle bisectors of  $ \angle C AB$  and  $ \angle AB C$  meet the sides  $ B C$  and  $ C A$  at  $ D$  and  $ E$  , respectively. Let  $ K$  be the incentre of triangle  $ ADC$ . Suppose that  $ \angle B E K \equal{} 45^\circ$  . Find all possible values of  $ \angle C AB$  .

*Jan Vonk, Belgium, Peter Vandendriessche, Belgium and Hojoo Lee, Korea*

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