
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, the equation of circle $C$ is given by 
$$
\begin{cases} 
x=1+ \sqrt {2}\cos \theta \\
y=1+ \sqrt {2}\sin \theta
\end{cases} 
(\theta \text{ is a parameter})
$$
With the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis, a polar coordinate system is established. The same unit length is taken in both coordinate systems. The polar equation of line $l$ is $\rho\cos \theta+\rho\sin \theta=m(m\in\mathbb{R})$.

(I) When $m=3$, determine the positional relationship between line $l$ and circle $C$;

(II) When there is exactly one point on $C$ such that the distance from this point to line $l$ equals $\sqrt {2}$, find the coordinates of the point(s) on $C$ whose distance to line $l$ is $2\sqrt {2}$.

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