
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 $l$: $\begin{cases} \left.\begin{matrix}x=5+ \frac { \sqrt{3}}{2}t \\\\ y= \sqrt{3}+ \frac{1}{2}t\end{matrix}\right.\end{cases}$ ($t$ is a parameter). Establish a polar coordinate system with the coordinate origin as the pole and the positive half of the $x$-axis as the polar axis. The polar equation of the curve $C$ is $ρ = 2\cos θ$.

(1) Convert the polar equation of the curve $C$ into a rectangular coordinate equation.
(2) Let the rectangular coordinates of point $M$ be $(5, \sqrt{3})$, and the intersection points of line $l$ and curve $C$ be $A$ and $B$. Find the value of $|MA| \cdot |MB|$.

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