
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 the center at the origin and a radius of $2$, for any point $P$ on the circle, a perpendicular line segment $PP'$ is drawn to the $x$-axis. The equation for the trajectory of the midpoint $M$ of the line segment $PP'$ is ________.

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