
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, the parametric equations of curve $C_{1}$ are $\left\{\begin{array}{l}x=1+t\\ y=1+2t\end{array}\right.$ (where $t$ is the parameter). Taking the coordinate origin as the pole and the positive $x$-axis as the polar axis, establish a polar coordinate system. The equation of curve $C_{2}$ is $\rho \left(1-\sin \theta \right)=1$. <br/> $(1)$ Find the general equation of curve $C_{1}$ and the rectangular coordinate equation of curve $C_{2}$; <br/> $(2)$ If point $M(0,-1)$, the intersection points of curves $C_{1}$ and $C_{2}$ are points $A$ and $B$, find the value of $|MA|\cdot |MB|$.

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