
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 $l$: $$\begin{cases}x=-2+\cos \alpha \cdot t \\ y=\sin \alpha \cdot t\end{cases} (t \text{ is a parameter}),$$ with the origin $O$ as the pole and the positive $x$-axis as the polar axis, a polar coordinate system is established. The polar equation of curve $C$ is $\rho=2\sin \theta - 2\cos \theta$.
(Ⅰ) Find the Cartesian equation of curve $C$;
(Ⅱ) When $\alpha= \frac{\pi}{4}$, find the length of the chord that line $l$ cuts from curve $C$.

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