
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 equations of the line $l$: 
$$\begin{cases}
   x = \frac{\sqrt{2}}{2}t \\
   y = \frac{\sqrt{2}}{2}t + 4\sqrt{2}
\end{cases} \quad (t \text{ is the parameter})$$
and the polar equation of the circle $C$: 
$$\rho = 4\cos\left(\theta + \frac{\pi}{4}\right).$$
(Ⅰ) Find the rectangular coordinates of the center of the circle $C$.
(Ⅱ) Tangents are drawn from a point on the line $l$ to the circle $C$. Find the minimum length of the tangents.

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