
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 point A (3, 0) is a point outside the circle $x^2+y^2=1$, and P is any point on the circle. If M is the midpoint of AP, find the equation of the trajectory of point M as P moves on the circle, and explain what curve it represents.

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