
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 \(AB = 5\), \(AD = 2\sqrt{3} + 2\), and \(\angle BAD = 30^\circ\). On the side \(AB\), a point \(K\) is taken such that \(AK: KB = 4:1\). A line is drawn through point \(K\) parallel to \(AD\). Inside the parallelogram, a point \(L\) is chosen on this line, and a point \(M\) is chosen on the side \(AD\) such that \(AM = KL\). The 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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