
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
Let  $P$  be a point outside the circle  $C$ . Find two points  $Q$  and  $R$  on the circle, such that  $P,Q$  and  $R$  are collinear and  $Q$  is the midpopint of the segmenet  $PR$ . (Discuss the number of solutions).

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