
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
A circle \(O\) with radius \(R\) is drawn on a piece of paper, and a point \(A\) inside the circle is given such that \(O A = a\). The paper is folded so that a point \(A^{\prime}\) on the circumference of the circle coincides with \(A\). Every such fold leaves a crease line. Find the set of points on all crease lines as \(A^{\prime}\) varies over all points on the circumference of the circle.

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