
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 $C_1$ is given by: 
$$
\begin{cases} 
x = 2\cos\alpha \\
y = 2 + 2\sin\alpha 
\end{cases}
$$
(where $\alpha$ is the parameter). In the polar coordinate system with the origin $O$ as the pole and the positive x-axis as the polar axis, the ray $\theta = \frac{2\pi}{3}$ intersects curve $C_1$ at a point different from the pole at point A, and intersects curve $C_2$ described by $\rho = 8\sin\theta$ at a point different from the pole at point B. Then the length of segment AB is __________.

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