
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 piece of paper has a circle with radius \( R \) and a fixed point \( A \) inside the circle such that \( \overline{OA} = a \). The paper is folded so that a point \( A' \) on the circumference coincides exactly with point \( A \), which leaves a crease. When \( A' \) is any point on the circumference, find the set of all points on all the crease lines.

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