
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
Given a circle with center $O$ and radius $r$ and a tangent $t$ at point $A$. Let $M$ be a point on the tangent $t$. Let $N$ be the point where the segment $OM$ intersects the circle. On the perpendicular to $t$ at $M$, measure a distance $MP = MN$ on the side of $t$ that does not contain the circle. What is the locus of points $P$ if $M$ runs along the tangent $t$?

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