
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 curve $C$ is $\begin{cases}x=2\cos \alpha \\ y=2+2\sin \alpha\end{cases}$ (where $\alpha$ is the parameter), and the parametric equation of line $l$ is $\begin{cases}x= \sqrt{3}- \dfrac{ \sqrt{3}}{2}t \\ y=3+ \dfrac{1}{2}t\end{cases}$ (where $t$ is the parameter). In the polar coordinate system with the origin $O$ as the pole and the positive $x$-axis as the polar axis, a ray passing through the pole $O$ intersects curve $C$ at a point $A$ different from the pole, and the polar coordinates of point $A$ are $(2 \sqrt{3} ,\theta)$, where $\theta\in\left( \dfrac{\pi}{2} ,\pi\right)$

(Ⅰ) Find the value of $\theta$;

(Ⅱ) If the ray $OA$ intersects line $l$ at point $B$, find the value of $|AB|$.

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