
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 $C$: $\dfrac{y^2}{a^2}+\dfrac{x^2}{b^2}=1$ ($a > b > 0$), the two foci of the ellipse are $F_1$ and $F_2$, respectively. A line perpendicular to the $y$-axis passing through point $F_1$ intersects the ellipse $C$ at points $M$ and $N$. The area of $\triangle MNF_2$ is $\sqrt{3}$, and the eccentricity of the ellipse $C$ is $\dfrac{\sqrt{3}}{2}$.

(Ⅰ) Find the standard equation of the ellipse $C$;

(Ⅱ) Given that $O$ is the origin, the line $l$: $y=kx+m$ intersects the $y$-axis at point $P$ and intersects the ellipse $C$ at two distinct points $A$ and $B$. If there exists a real number $\lambda$, such that $\overrightarrow{OA}+\lambda \overrightarrow{OB}=4\overrightarrow{OP}$, find the range of values for $m$.

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