
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 the ellipse $C:\dfrac{x^{2}}{4}+\dfrac{y^{2}}{3}=1$ with its left and right vertices as $A$ and $B$, respectively, and $F$ as the right focus of the ellipse $C$. There is a moving point $P$ on the circle $x^{2}+y^{2}=4$, where $P$ is different from points $A$ and $B$. The line $PA$ intersects the ellipse $C$ at point $Q$ (different from point $A$). If the slope of line $QF$ exists, then the range of $\dfrac{k_{{PB}}}{k_{{QF}}}$ is \_\_\_\_.

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