
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 by the parametric equations $$C: \begin{cases} x=\cos{\alpha} \\ y=\sqrt{3}\sin{\alpha} \end{cases}$$ 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) The line $l_1$ passes through point $M(0, -1)$ and is parallel to line $l$. It intersects curve $C$ at points $A$ and $B$. Find the distance of line segment $AB$.

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