
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 parametric equation of circle $C$ is 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 that has the same unit length as the cartesian coordinate system $(xoy)$, with the origin $O$ as the pole and the non-negative half of the $x$-axis as the polar axis, the equation of line $l$ is given by $\sqrt {2}\rho\sin (\theta- \frac {\pi}{4})=m$ ($m\in\mathbb{R}$).

(1) Find the standard equation of circle $C$ and the cartesian coordinate equation of line $l$.

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

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