
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
On the bisector  $AL$  of triangle  $ABC$  a point  $K$  is chosen such that  $\angle BKL=\angle KBL=30^{\circ}$ . Lines  $AB$  and  $CK$  intersect at point  $M$ , lines  $AC$  and  $BK$  intersect at point  $N$ . FInd the measure of angle  $\angle AMN$ *Proposed by D. Shiryaev, S. Berlov*

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