
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 $x^{2}+y^{2}=9$, from any point $P$ on this circle, a perpendicular line segment $PP'$ is drawn to the $x$-axis. Point $M$ is on $PP'$, and $\overrightarrow{PM}=2\overrightarrow{MP'}$. Find the trajectory of point $M$.

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