
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 
$$
\begin{cases} 
x=2\cos\alpha \\
y=2+2\sin\alpha 
\end{cases}
$$
($\alpha$ is the parameter), and the parametric equation of line $l$ is 
$$
\begin{cases} 
x= \sqrt {3}- \frac { \sqrt {3}}{2}t \\
y=3+ \frac {1}{2}t
\end{cases}
$$
($t$ 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 point $A$ different from the pole, and the polar coordinates of point $A$ are $(2\sqrt {3}, \theta)$, where $\theta\in\left(\frac {\pi}{2}, \pi\right)$  
(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}
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