
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
An acute angle with the vertex  $O$  and the rays  $Op_1$  and  $Op_2$  is given in a plane. Let  $k_1$  be a circle with the center on  $Op_1$  which is tangent to  $Op_2$ . Let  $k_2$  be the circle that is tangent to both rays  $Op_1$  and  $Op_2$  and to the circle  $k_1$  from outside. Find the locus of tangency points of  $k_1$  and  $k_2$  when center of  $k_1$  moves along the ray  $Op_1$ .


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