
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 rectangular coordinate system on a plane, with the origin as the pole and the non-negative semi-axis of the x-axis as the polar axis, the polar coordinate equations of the line $l$ and the ellipse $C$ are given by $ρ\cos θ+2ρ\sin θ+3 \sqrt {2}=0$ and $ρ^{2}= \dfrac {4}{\cos ^{2}θ +4\sin ^{2}θ }$, respectively.
(1) Find the rectangular coordinate equations of line $l$ and ellipse $C$;
(2) If $P$ is a moving point on line $l$ and $Q$ is a moving point on ellipse $C$, find the minimum value of $|PQ|$.

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