
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
Given the angles of triangle ABC and the radius R of the circumscribed circle passing through the vertices, connect the feet of the altitudes of the triangle. Calculate the sides, angles, and the circumradius of the triangle formed by these feet (the orthic triangle).

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