
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
On a piece of paper, there is a circle with a radius $R$ centered at $O$ and an internal point $A$ such that $OA = a$. Fold the paper so that a point $A'$ on the circumference of the circle coincides with point $A$. Each such fold leaves a crease, which is a straight line. Determine the set of all points on the crease lines when $A'$ has taken every point on the circumference of the circle.

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