
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 parallelogram \(ABCD\) (\(AB \ne BC\)), two altitudes, \(BH\) and \(BK\), are drawn from the obtuse angle \(B\) (the bases of the altitudes lie on the sides of the parallelogram and do not coincide with its vertices). The triangle \(BHK\) is isosceles. Determine all possible values of the angle \(BAD\).

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