
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 that the pole of the polar coordinate system coincides with the origin of the rectangular coordinate system, and the polar axis coincides with the positive semi-axis of the x-axis, if the polar coordinate equation of the line $l$ is $ρ \sin (θ- \frac{π}{4} )=2 \sqrt{2}$.

(1) Convert the polar coordinate equation of line $l$ to a rectangular coordinate system equation;

(2) Given that $P$ is a point on the ellipse $C$: $\frac{{x}^{2}}{3}+ \frac{{y}^{2}}{9}=1$, find the minimum value of the distance from $P$ to line $l$.

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