
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 circle $O: x^{2}+y^{2}=4$ intersect the $y$-axis at points $A$ and $B$ ($A$ is above $B$). Let line $l$ be tangent to circle $O$ at point $B$. If the distance from moving point $P$ to $A$ is equal to the distance from $P$ to line $l$, determine the equation of the trajectory of point $P$.

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