
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 polar coordinate system, it is known that circle $C: \rho = \cos \theta + \sin \theta$, and line $l: \rho = \frac{2\sqrt{2}}{\cos (\theta + \frac{\pi}{4})}$.

(Ⅰ) Taking the pole $O$ as the origin and the positive half-axis of the $x$-axis as the polar axis, establish a Cartesian coordinate system and find the Cartesian equation of circle $C$;

(Ⅱ) Find the minimum distance from a point on circle $C$ to line $l$.

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