
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 parametric equation of line $l$ as $\begin{cases}x=1+ \frac{ \sqrt{2}}{2}t \\ y=-1+ \frac{ \sqrt{2}}{2}t\end{cases} (t\text{ is the parameter})$, establish a polar coordinate system with the coordinate origin as the pole and the positive half of the $x$-axis as the polar axis. The polar coordinate equation of circle $C$ is $\rho=2(\cos \theta-\sin \theta)$.

(I) Find the Cartesian coordinate equation of circle $C$.
(II) If $P(x,y)$ is the common point of line $l$ and the circle surface $\rho\leqslant 2(\cos \theta- \sin \theta)$, find the range of values for $x+y$.

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