
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
Given a parallelogram \(ABCD\) with \(AB = 3\), \(AD = \sqrt{3} + 1\), and \(\angle BAD = 60^\circ\). A point \(K\) is taken on side \(AB\) such that \(AK : KB = 2 : 1\). A line parallel to \(AD\) is drawn through point \(K\). On this line, inside the parallelogram, point \(L\) is selected, and on side \(AD\), point \(M\) is chosen such that \(AM = KL\). Lines \(BM\) and \(CL\) intersect at point \(N\). Find the angle \(BKN\).

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