
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 $(xOy)$, establish a polar coordinate system with $O$ as the pole and the positive semi-axis of $x$ as the polar axis. Given the line $l$: $\sqrt {2}\rho\sin (θ- \frac {π}{4})=m (m\in R)$, and the parametric equation of the circle $C$ is $\begin{cases} x=1+3\cos t \\ y=-2+3\sin t \end{cases} (t\text{ is the parameter})$. Find the value of $m$ when the distance from the center of the circle $C$ to the line $l$ is $\sqrt {2}$.

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