
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
An equilateral triangle is inscribed in a circle. Find the geometric locus of the points of intersection of the altitudes of all possible triangles inscribed in the same circle, with two sides parallel to two sides of the given equilateral triangle.

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