
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 Cartesian coordinate system $xoy$, with the origin as the pole and the positive $x$-axis as the polar axis, a polar coordinate system is established. It is known that the polar equation of a certain circle is: ${{\rho }^{2}}-4\rho \cos \theta +2=0$.

$(1)$ Convert the polar equation into a standard equation;

$(2)$ If point $P(x,y)$ is on the circle, find the maximum and minimum values of $x+y$.

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