
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
Assume $A$ and $B$ are two foci of the ellipse $C: \dfrac{x^{2}}{4}+\dfrac{y^{2}}{k}=1$. If there exists a point $P$ on $C$ such that $\angle APB=120^{\circ}$, then determine the range of $k$.

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