
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
Let point $P$ be any point on the circle $x^{2}+y^{2}=1$. From point $P$, a perpendicular line $PP_{0}$ is drawn to the $x$-axis, with $P_{0}$ as the foot of the perpendicular, and $\overrightarrow{MP_{0}}=\frac{{\sqrt{3}}}{2}\overrightarrow{PP_{0}}$. Find the equation of the locus $C$ of point $M$ ______.

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