
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
Elective 4-4: Coordinate System and Parametric Equations

In the Cartesian coordinate system $xOy$, the parametric equation of line $l$ is $\begin{cases} x=1-\dfrac{\sqrt{2}}{2}t \\ y=4-\dfrac{\sqrt{2}}{2}t \end{cases}$ ($t$ is the parameter), and a polar coordinate system is established with the origin as the pole and the positive $x$-axis as the polar axis, which has the same unit of length as the Cartesian coordinate system. In this polar coordinate system, the equation of circle $C$ is $\rho =-4\cos \theta$.

(Ⅰ) Find the Cartesian coordinate equation of circle $C$;

(Ⅱ) Suppose circle $C$ intersects line $l$ at points $A$ and $B$. If the coordinates of point $M$ are $(-2,1)$, find the value of $|MA|\cdot |MB|$.

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