
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 parametric equation of line $l$ as $ \begin{cases} x=-2+ \frac { \sqrt {6}}{3}t \\ y= \frac { \sqrt {3}}{3}t \end{cases} (t \text{ is the parameter})$, in the rectangular coordinate system, establish a polar coordinate system with the origin $O$ as the pole and the positive semi-axis of $x$ as the polar axis. The equation of curve $C$ is $ρ=2 \sqrt {2}\cos (θ- \frac {π}{4})-2\sin θ$.
$(1)$ Find the rectangular coordinate equation of curve $C$.
$(2)$ Points $P$ and $Q$ are moving points on line $l$ and curve $C$, respectively. Find the range of values for $|PQ|$.

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