
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
In the plane rectangular coordinate system $xOy$, given the circle $O: x^{2}+y^{2}=3$, the coordinates of points $M$ and $M'$ are $({\sqrt{2},0})$ and $({-\sqrt{2},0})$ respectively. Let $N$ be a point in the plane such that the circle with diameter $MN$ is tangent to circle $O$. The locus of point $N$ is denoted as curve $C$.  
$(1)$ Find the equation of curve $C$;  
$(2)$ Given that $P$ is a point on curve $C$, two tangents are drawn from the origin $O$ to a circle with center $P$ and radius $\frac{{\sqrt{3}}}{2}$, intersecting curve $C$ at points $A$ and $B$. Determine whether $|OA|^{2}+|OB|^{2}$ is a constant value. If it is, find the constant value; if not, explain the reason.

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