
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 point $C$ is the center of the circle $(x+1)^{2}+y^{2}=8$, and $P$ is a moving point on the circle. Point $Q$ is on the radius $CP$, and there are point $A(1,0)$ and a point $M$ on $AP$, satisfying $\overrightarrow{MQ} \cdot \overrightarrow{AP}=0$, $\overrightarrow{AP}=2 \overrightarrow{AM}$.  
(Ⅰ) When point $P$ moves on the circle, determine the trajectory of point $Q$ and find its equation;  
(Ⅱ) If a line $l$ with slope $k$ is tangent to the circle $x^{2}+y^{2}=1$ and intersects the trajectory of point $Q$ found in (Ⅰ) at two distinct points $F$, $H$, and $ \dfrac {3}{4}\leqslant \overrightarrow{OF}\cdot \overrightarrow{OH}\leqslant \dfrac {4}{5}$ (where $O$ is the origin), find the range of $k$.

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