
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 a circle, point  $C$  on it and point  $A$  outside the circle. The equilateral triangle  $ACP$  is constructed on the segment  $AC$ . Point  $C$  moves along the circle. What trajectory will the point  $P$  describe?

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