
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, using the origin O as the pole and the positive semi-axis of the x-axis as the polar axis, the curve C has the parametric equation:
$$
\begin{cases}
x = 2\cos\phi \\
y = 2 + 2\sin\phi
\end{cases}
(\text{ where } \phi \text{ is the parameter}).
$$
Points A and B are two points on curve C, with polar coordinates of $A(\rho_1, \frac{\pi}{3})$ and $B(\rho_2, \frac{5\pi}{6})$, respectively. Find the distance $|AB|$.

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