
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 $l$: 
$$
\begin{cases} 
x=5+ \frac { \sqrt {3}}{2}t \\
y= \sqrt {3}+ \frac {1}{2}t
\end{cases}
(t \text{ is the parameter})
$$
with the origin as the pole and the positive half-axis of $x$ as the polar axis to establish a polar coordinate system, the polar equation of curve $C$ is $\rho=2\cos \theta$. Let the rectangular coordinates of point $M$ be $(5, \sqrt {3})$, and the intersection points of line $l$ with curve $C$ are $A$ and $B$, calculate the value of $|MA|\cdot|MB|$.

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