
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
All angles of  $ABC$  are in  $(30,90)$ . Circumcenter of  $ABC$  is  $O$  and circumradius is  $R$ . Point  $K$  is projection of  $O$  to angle bisector of  $\angle B$ , point  $M$  is midpoint  $AC$ . It is known, that  $2KM=R$ . Find  $\angle B$ 

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