
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 $C:\frac{{x}^{2}}{{a}^{2}}+{y}^{2}=1(a＞1)$ with eccentricity $e=\frac{\sqrt{3}}{2}$, where points $M$ and $N$ are two distinct moving points on the ellipse.<br/>$(1)$ Find the standard equation of the ellipse $C$;<br/>$(2)$ If the line $MN$ passes through the point $Q\left(0,2\right)$ and $\overrightarrow{OM}⋅\overrightarrow{ON}＞0$, with the midpoint of segment $MN$ being $P$, find the range of slopes for the line $OP$.

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