
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 $xOy$, the curve $C$ is defined by the parametric equations $\begin{cases} x= \sqrt {2}\cos\alpha+1 \\ y= \sqrt {2}\sin\alpha+1 \end{cases}$ (where $\alpha$ is a parameter). In the polar coordinate system with the origin $O$ as the pole and the non-negative half-axis of the $x$-axis as the polar axis, the polar equation of line $l$ is $\rho\sin(\theta+ \frac {\pi}{4})=m$ (where $m\in\mathbb{R}$).  
(I) Find the Cartesian equation of line $l$;  
(II) If there exists a point $P$ on curve $C$ such that the distance from $P$ to line $l$ is $\frac { \sqrt {2}}{2}$, find the range of the real number $m$.

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