
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 center of the circle  $\omega$  circumscribed around the acute-angled triangle  $\vartriangle ABC$ , and  $W$  be the midpoint of the arc  $BC$  of the circle   $\omega$ , which does not contain the point  $A$ , and  $H$  be the point of intersection of the heights of the triangle   $\vartriangle ABC$ . Find the angle  $\angle BAC$ , if  $WO = WH$ .

(O. Clurman)

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