
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 curve $C_{1}$: $\begin{cases} x=t\cos \alpha \\ y=t\sin \alpha \end{cases}$ (with $t$ as the parameter, $t\neq 0$), where $0\leqslant \alpha < \pi$, in the polar coordinate system with $O$ as the pole and the positive half-axis of $x$ as the polar axis, the curve $C_{2}$: $\rho=2\sin \theta$, and the curve $C_{3}$: $\rho=2 \sqrt {3}\cos \theta$.  
(Ⅰ) Find the Cartesian coordinates of the intersection points of $C_{2}$ and $C_{3}$;  
(Ⅱ) If $C_{2}$ intersects with $C_{1}$ at point $A$, and $C_{3}$ intersects with $C_{1}$ at point $B$, find the maximum value of $|AB|$.

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