
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 a triangle  $ABC$ , and let  $l$  be the line going through the midpoint of the side  $BC$  and is perpendicular to the bisector of  $\angle BAC$ . Determine the value of  $\angle BAC$  if the line  $l$  goes through the midpoint of the line segment  $AO$ .

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