
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 $\begin{cases} x=2\sqrt{3}-\frac{\sqrt{3}}{2}t \\ y=\frac{1}{2}t \end{cases}$ (where $t$ is the parameter), and the parametric equation of curve $C$ is $\begin{cases} x=\sqrt{3}+\sqrt{3}\cos \alpha \\ y=\sqrt{3}\sin \alpha \end{cases}$ (where $\alpha$ is the parameter). Establish a polar coordinate system with the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis.  
(Ⅰ) Find the polar equations of line $l$ and curve $C$;  
(Ⅱ) Given that a point $M$ on line $l$ has polar coordinates $(2,\theta)$, where $\theta\in(0, \frac{\pi}{2})$. The ray $OM$ intersects curve $C$ at a point $N$ different from the pole, find the value of $|MN|$.

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