
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 $xOy$, with $O$ as the pole and the positive half-axis of the $x$-axis as the polar axis, a polar coordinate system is established. The equation of line $l$ is $\sqrt{2}\rho\sin(\theta - \frac{\pi}{4}) = m$ ($m \in \mathbb{R}$), and the parametric equation of circle $C$ is $\begin{cases} x=1+3\cos t \\ y=-2+3\sin t \end{cases}$ (where $t$ is the parameter). When the distance from the center of circle $C$ to line $l$ is $\sqrt{2}$, find the value of $m$.

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