
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
Given the parametric equation of line $l$ as $\begin{cases} x=\frac{\sqrt{2}}{2}t \\ y=\frac{\sqrt{2}}{2}t+4\sqrt{2} \end{cases}$ (where $t$ is the parameter), and the polar coordinate equation of circle $C$ as $\rho =2\cos (\theta +\frac{\mathrm{\pi }}{4})$:

(I) Find the rectangular coordinates of the center of circle $C$;

(II) Find the minimum length of a tangent line drawn from a point on line $l$ to circle $C$.

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