
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 \(AB = AC\). The angle bisectors of \(A\) and \(B\) meet the sides \(BC\) and \(AC\) in \(D\) and \(E\), respectively. Let \(K\) be the incenter of triangle \(ADC\). Suppose that \(\angle BEK = 45^\circ\). Find all possible values of \(\angle BAC\).

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