
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 an ellipse $E:\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1(a>b>0)$, the area of the quadrilateral formed by the intersection points of the ellipse with the coordinate axes is $4\sqrt{3}$, and the minimum distance from any point on $E$ to one of its foci is $1$.  
$(1)$ Find the equation of the ellipse $E$.  
$(2)$ Let the line $l:y=kx+m(0≤k≤\sqrt{3})$ intersect $E$ at points $M$ and $N$, with $O$ as the origin. Form a parallelogram $OMPN$ with sides $OM$ and $ON$, where $P$ lies on the ellipse $E$. Find the range of values for $|OP|$.

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