
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 that the polar coordinate equation of curve $C$ is $\rho -4\cos \theta +3\rho \sin ^{2}\theta =0$, establish a rectangular coordinate system with the pole as the origin and the polar axis as the positive $x$-axis. A line $l$ passes through point $M(1,0)$ with an inclination angle of $\frac{\pi }{6}$.

(I) Find the rectangular coordinate equation of curve $C$ and the parametric equation of line $l$;

(II) If curve $C$ undergoes a stretch transformation $\begin{cases} x'=x \ \ y'=2y \end{cases}$ to obtain curve $C'$, and line $l$ intersects curve $C'$ at points $A$ and $B$, find $|MA|+|MB|$.

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