
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
A line perpendicular to the $x$-axis passes through point $M$ on circle $C$: $x^{2}+y^{2}=4$, and intersects the $x$-axis at point $N$. Point $P$ satisfies $\overrightarrow{NP}= \dfrac {\sqrt {3}}{2} \overrightarrow{NM}$. As $M$ moves on circle $C$, the trajectory of point $P$ is denoted as $E$.  
$(1)$ Find the equation of $E$;  
$(2)$ A line through point $Q(0,1)$ intersects $E$ at points $A$ and $B$, and intersects circle $C$ at points $S$ and $T$. Find the range of values for $|AB|\cdot|ST|$.

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