
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
Two circles with radius 1 intersect at points $X$ and $Y$, with a distance of 1 between them. From point $C$ on one circle, tangents $CA$ and $CB$ are drawn to the other circle. Line $CB$ intersects the first circle again at point $A'$. Find the distance $AA'$.

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