
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 $(xoy)$, the equation of line $l$ is $x-y+4=0$. In the polar coordinate system with the origin $O$ as the pole and the positive half of the $x$-axis as the polar axis, the polar equation of curve $C$ is $ρ^{2}-4 \sqrt {2}ρ\cos (θ- \frac {π}{4})+6=0$.

1. Find the polar equation of line $l$ and the rectangular equation of curve $C$.
2. If point $P$ is any point on curve $C$ with rectangular coordinates $(x, y)$, find the maximum and minimum values of $x+2y$.

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