
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  $O$  be the circumcenter of triangle  $ABC$ , and let  $l$  be the line passing through the midpoint of segment  $BC$  which is also perpendicular to the bisector of angle  $ \angle BAC $ . Suppose that the midpoint of segment  $AO$  lies on  $l$ . Find  $ \angle BAC $ .

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