
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
 $k_1$  denotes one of the arcs formed by intersection of the circumference  $k$  and the chord  $AB$ .  $C$  is the middle point of  $k_1$ . On the half line (ray)  $PC$  is drawn the segment  $PM$ . Find the locus formed from the point  $M$  when  $P$  is moving on  $k_1$ .

*G. Ganchev*

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