
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 point $A(0,\sqrt{3})$ and circle $O_1: x^2+(y+ \sqrt{3})^2=16$, point $M$ moves on circle $O_1$, and point $P$ is on the radius $O_1M$ with $|PM|=|PA|$. Find the equation of the trajectory of the moving point $P$.

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