
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 radii 1 meet in points  $X, Y$ , and the distance between these points also is equal to  $1$ . Point  $C$  lies on the first circle, and lines  $CA, CB$  are tangents to the second one. These tangents meet the first circle for the second time in points  $B', A'$ . Lines  $AA'$  and  $BB'$  meet in point  $Z$ . Find angle  $XZY$ .

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