
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 polar coordinate equation of a circle is $ρ^{2}-4 \sqrt {2}ρ\cos (θ- \frac {π}{4})+6=0$, find:

1. The ordinary equation and a parametric equation of the circle;
2. The maximum and minimum values of $xy$ among all points $(x, y)$ on the circle.

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