
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 plane rectangular coordinate system $xOy$, the parametric equations of curve $C$ are $\left\{\begin{array}{l}x=\sqrt{3}\cos\alpha\\ y=\sqrt{3}\sin\alpha\end{array}\right.$ ($\alpha$ is the parameter). Taking the coordinate origin as the pole and the positive $x$-axis as the polar axis, the polar coordinate equation of the line $l$ is $\rho \cos \theta -\rho \sin \theta +1=0$. <br/>$(1)$ Find the Cartesian equation of curve $C$ and the rectangular coordinate equation of line $l$; <br/>$(2)$ Line $l$ intersects curve $C$ at two distinct points $A$ and $B$, and intersects the $y$-axis at point $M$. Find the value of $|MA|\cdot |MB|$.

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