
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 equations of curve $C_{1}$ are $\left\{\begin{array}{l}{x=2+2\cos\varphi}\\{y=2\sin\varphi}\end{array}\right.$ ($\varphi$ is the parameter). Taking the origin $O$ as the pole and the positive half of the $x$-axis as the polar axis, the polar equation of curve $C_{2}$ is $\rho =4\sin \theta$. <br/>$(Ⅰ)$ Find the general equation of curve $C_{1}$ and the Cartesian equation of $C_{2}$; <br/>$(Ⅱ)$ Given that the polar equation of curve $C_{3}$ is $\theta =\alpha$, $0 \lt \alpha\ \ \lt \pi$, $\rho \in R$, point $A$ is the intersection point of curves $C_{3}$ and $C_{1}$, point $B$ is the intersection point of curves $C_{3}$ and $C_{2}$, and both $A$ and $B$ are different from the origin $O$, and $|AB|=4\sqrt{2}$, find the value of the real number $\alpha$.

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