
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
Let  $I$  and  $H$  be the incenter and orthocenter of an acute triangle  $ABC$ .  $M$  is the midpoint of arc  $AC$  of circumcircle of triangle  $ABC$  which does not contain point  $B$ . If  $MI=MH$ , find the measure of angle  $\angle ABC$ .


*Proposed by F. Bakharev*

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