
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  $ABC$  be an acute-angled, not equilateral triangle, where vertex  $A$  lies on the perpendicular bisector of the segment  $HO$ , joining the orthocentre  $H$  to the circumcentre  $O$ . Determine all possible values for the measure of angle  $A$ .

(U.S.A. - 1989 IMO Shortlist)

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