
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
A point  $ M$  is taken on the perpendicular bisector of the side  $ AC$  of an acute-angled triangle  $ ABC$  so that  $ M$  and  $ B$  are on the same side of  $ AC$ . If  $ \angle BAC\equal{}\angle MCB$  and  $ \angle ABC\plus{}\angle MBC\equal{}180^{\circ}$ , find  $ \angle BAC.$ 

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