
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 \( O \) with radius \( R \) and a point \( A \) inside the circle 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 line. When \( A' \) takes all possible positions on the circumference, find the set of all points on these crease lines.

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