
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
In the polar coordinate system, points $A(\sqrt{3}, \frac{\pi}{6})$, $B(\sqrt{3}, \frac{\pi}{2})$, and line $l$ is parallel to line $AB$ and bisects the area enclosed by the curve $C$: $\rho=2\cos(\theta- \frac{\pi}{3}) (\rho\geqslant 0)$. Establish a Cartesian coordinate system with the pole as the origin and the polar axis as the positive half-axis of $x$.

(Ⅰ) In the Cartesian coordinate system, find the parametric equations of curve $C$ and line $l$;

(Ⅱ) Let point $M$ be a moving point on curve $C$, find the range of values for $|MA|^{2}+|MB|^{2}$.

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