
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 that point P is a moving point on the circle $x^2+y^2=16$, and point A is a fixed point on the x-axis with coordinates $(12,0)$. Find the equation of the trajectory of the midpoint M of segment PA as point P moves on the circle.

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