
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
In a plane, let \( c \) be a circle, and let line \( l \) be a tangent to the circle. Point \( M \) is on line \( l \). Find the set of all points \( P \) such that there exist two points \( Q \) and \( R \) on line \( l \) with the property that \( M \) is the midpoint of segment \( QR \) and \( c \) is the incircle of triangle \( PQR \).

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