
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 equation of circle $C$ as $\rho = 2\cos (\theta + \frac{\pi}{4})$,

(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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