
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 Cartesian coordinate system $xoy$, the curve $C$ is defined parametrically as follows: $$\begin{cases} x=\sqrt{3}\cos \alpha \\ y=\sin \alpha \end{cases}$$ where $\alpha$ is a parameter. In the polar coordinate system with the origin $O$ as the pole and the non-negative half of the $x$-axis as the polar axis, the polar equation of the line $l$ is given by $\frac{\sqrt{2}}{2}\rho \cos (\theta + \frac{\pi }{4})=-1$.

(1) Find the Cartesian equation of the curve $C$ and the polar equation of the line $l$.
(2) A line ${l}^{{'}}$ passes through the point $M(-1,0)$ and is parallel to the line $l$. Find the distance $| AB |$ between the points $A$ and $B$ where ${l}^{{'}}$ intersects the curve $C$, as well as the product $| MA | \cdot | MB |$.

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