
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
Consider a point $P$ on the circle $x^2 + y^2 = 16$. Draw a perpendicular line segment $PD$ from point $P$ to the $x$-axis, with $D$ being the foot of the perpendicular. As point $P$ moves on the circle, find the equation of the trajectory of the midpoint $M$ of line segment $PD$.

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