
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 $({ρ}^{2}-4 \sqrt{2}ρ\cos \left(θ- \dfrac{π}{4}\right)+6=0 )$, find:

(1) The ordinary equation and parametric equation of the circle;

(2) The points on the circle that maximize and minimize the value of $x+y$, and find these extreme values.

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