
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
Let a moving point $M(x, y)$ have a distance to the line $y=3$ and its distance to the point $F(0, 1)$ in the ratio of $\sqrt{3}$. The trajectory of point $M$ is curve $E$.

(Ⅰ) Find the equation of curve $E$:

(Ⅱ) A line $l$ passing through point $F$ intersects curve $E$ at points $A$ and $B$, and $\overrightarrow{AF}=\lambda \overrightarrow{FB}$. When $2\leqslant \lambda\leqslant 3$, find the range of values for the slope $k$ of line $l$.

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