
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 $l$: $\begin{cases}x=2+ \frac{1}{2}t \\ y= \sqrt{3}+ \frac{ \sqrt{3}}{2}t\end{cases} (t$ is a parameter), establish a polar coordinate system with the origin as the pole and the positive half of the $x$-axis as the polar axis. The polar coordinate equation of the curve $C$ is $\rho=2$.
(I) If the rectangular coordinates of point $M$ are $(2,\sqrt{3} )$, and line $l$ intersects curve $C$ at points $A$ and $B$, find the value of $|MA|+|MB|$;
(II) Suppose curve $C$ undergoes a stretch transformation $\begin{cases}x'= \sqrt{3}x \\ y'=y\end{cases} $ to obtain curve $C'$, find the maximum value of the perimeter of the inscribed rectangle of curve $C'$.

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