
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 triangle  $ABC$ . Point  $M$  is the projection of vertex  $B$  to bisector of angle  $C$ .  $K$  is the touching point of the incircle with side  $BC$ . Find angle  $\angle  MKB$  if  $\angle BAC = \alpha$ (V.Protasov) 

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