
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 Cartesian coordinate system $xOy$, the parametric equation of line $l$ is $\begin{cases} & x=3+\dfrac{1}{2}t \\ & y=\dfrac{\sqrt{3}}{2}t \\ \end{cases}$ ($t$ is the parameter). With the origin as the pole and the positive half-axis of $x$ as the polar axis, the polar equation of $\odot C$ is $\rho =2\sqrt{3}\sin \theta$.

(Ⅰ) Write the Cartesian coordinate equation of $\odot C$;

(Ⅱ) Let $R$ be a moving point on line $l$, when the distance from $R$ to the center $C$ is minimized, find the Cartesian coordinates of $R$.

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