
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
Given the line $l: \begin{cases} & x=5+\frac{\sqrt{3}}{2}t \\ & y=\sqrt{3}+\frac{1}{2}t \\ \end{cases} (t$ is a parameter), with the origin as the pole and the positive half-axis of $x$ as the polar axis, establish a polar coordinate system. The polar equation of curve $C$ is $\rho =2\cos \theta$.

(Ⅰ) Convert the polar equation of curve $C$ into a Cartesian coordinate equation;

(Ⅱ) Suppose the Cartesian coordinates of point $M$ are $(5,\sqrt{3})$, and the intersection points of line $l$ with curve $C$ are $A$ and $B$. Find the value of $|MA|\cdot |MB|$.

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