
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 $C_{1}$ is defined by $\begin{cases}x=t\cos \alpha \\ y=t\sin \alpha\end{cases} (t$ is a parameter, $t\neq 0)$, where $0\leqslant \alpha < \pi$. In the polar coordinate system with $O$ as the pole and the positive $x$-axis as the polar axis, the curve $C_{2}$ is defined by $\rho=4\sin \theta$, and the curve $C_{3}$ is defined by $\rho=4 \sqrt{3}\cos \theta$.
(Ⅰ) Find the Cartesian coordinates of the intersection points of $C_{2}$ and $C_{3}$;
(Ⅱ) If $C_{2}$ intersects $C_{1}$ at point $A$, and $C_{3}$ intersects $C_{1}$ at point $B$, find the maximum value of $|AB|$.

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