
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 point $M$ on the circle $C: x^2 + y^2 = 4$ has a perpendicular line drawn to the $x$-axis, intersecting it at point $N$. Point $P$ satisfies $\overrightarrow{NP} = \frac{\sqrt{3}}{2}\overrightarrow{NM}$. As point $M$ moves along the circle $C$, the trajectory of point $P$ forms a curve $E$.

(1) Find the equation of curve $E$.
(2) A line $l$ passing through point $Q(0, 1)$ intersects curve $E$ at points $A$ and $B$, and 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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