
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 the line $l$ is 
$$
\left\{ 
\begin{aligned} 
& x=2\sqrt{3}-\frac{\sqrt{3}}{2}t \\
& y=\frac{1}{2}t 
\end{aligned}
\right. (t \text{ is a parameter}),
$$
and the parametric equation of curve $C$ is 
$$
\left\{ 
\begin{aligned}
& x=\sqrt{3}+\sqrt{3}\cos \alpha \\
& y=\sqrt{3}\sin \alpha 
\end{aligned}
\right. (\alpha \text{ is a parameter}).
$$
Take the origin $O$ as the pole and the positive half-axis of $x$ as the polar axis to establish the polar coordinate system.

(Ⅰ) Find the polar equations of the line $l$ and the curve $C$;

(Ⅱ) It is known that the polar coordinate of a point $M$ on line $l$ is $(2,\theta)$, where $\theta \in \left(0,\frac{\pi}{2}\right)$. The ray $OM$ intersects curve $C$ at point $N$, which is distinct from the pole. Find the value of $|MN|$.

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