
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 that the two foci of ellipse $C$ are ${F}_{1}(0,-\sqrt{3})$ and ${F}_{2}(0,\sqrt{3})$, and ellipse $C$ passes through point $M(\frac{\sqrt{3}}{2},1)$.  
$(1)$ Find the standard equation of ellipse $C$;  
$(2)$ If point $P$ is any point on ellipse $C$, find the range of $\frac{1}{|P{F}_{1}|}+\frac{1}{|P{F}_{2}|}$.

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