
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 that the polar equation of line $l$ is $\rho \sin \left( \theta + \frac{\pi}{4} \right) = \frac{\sqrt{2}}{2}$, and the parametric equation of circle $C$ is $\begin{cases} x = 2\cos\theta \\ y = -2 + 2\sin\theta \end{cases}$ (where $\theta$ is the parameter),
(Ⅰ) Determine the positional relationship between line $l$ and circle $C$;
(Ⅱ) If the parametric equation of the ellipse is $\begin{cases} x = 2\cos\varphi \\ y = \sqrt{3}\sin\varphi \end{cases}$ (where $\varphi$ is the parameter), find the product of the lengths $|CA|$ and $|CB|$, where line $l'$ passes through the center of circle $C$, is perpendicular to line $l$, and intersects the ellipse at points A and B.

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