
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, a circle $O$ with radius $R$ and a point $A$ inside the circle (such that $OA = a$) are drawn. The paper is folded so that a point $A'$, located on the circumference of the circle, coincides with point $A$. Each unique way of folding leaves a straight crease. Find the set of all points on these creases when $A'$ takes all possible positions on the circumference of the circle.

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