
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
In the Cartesian coordinate system $xOy$, with the origin as the pole and the positive $x$-axis as the polar axis, we establish a polar coordinate system. Given the curve $C: \rho^{2}= \dfrac {4}{1+\sin ^{2}\theta }$ where $\theta \in [0,\pi]$, and the line $l$ defined by the parametric equations $\begin{cases} x=5-2 \sqrt {3}t \\ y=t \end{cases}$ (with $t$ as the parameter).
$(1)$ Find the parametric equations of curve $C$ and the general equation for line $l$;
$(2)$ Let point $P$ lie on curve $C$ and point $Q$ on line $l$. Determine the range of values for $|PQ|$.

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