
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 rectangular coordinate system $(xOy)$, the parametric equations of circle $C$ are given by $\begin{cases} & x=1+3\cos t \\ & y=-2+3\sin t \end{cases}$ $(t$ is the parameter$)$. In the polar coordinate system $((r,\theta))$, which has the same unit length as the rectangular coordinate system $(xOy)$, and takes the origin $O$ as the pole and the non-negative half-axis of $x$ as the polar axis, the equation of line $l$ is given by $\sqrt{2}r\sin(\theta-\frac{\pi}{4})=m$ $(m\in\mathbb{R})$.

(I) Find the general form equation of circle $C$ and the rectangular coordinate equation of line $l$;

(II) If the distance from the center of circle $C$ to line $l$ is $2$, find the value of $m$.

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