
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 $xOy$, with the origin $O$ as the pole and the $x$-axis as the polar axis, a polar coordinate system is established. It is known that the line $l$ is defined by $\begin{cases} x= \frac { \sqrt {2}}{2}t \\ y=-1+ \frac { \sqrt {2}}{2}t\end{cases}$ (where $t$ is a parameter), and the polar equation of curve $C$ is $\rho^{2}-6\rho\cos \theta+1=0$. Line $l$ intersects curve $C$ at two points $A$ and $B$.
$(1)$ Find the standard equation of line $l$ and the Cartesian equation of curve $C$;
$(2)$ Given $M(0,-1)$, find the value of $|MA|\cdot|MB|$.

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