
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
Given the parametric equations of curve $C\_1$ as: $\begin{cases} x=\cos \theta \ y=1+\sin \theta \end{cases}$ (where $\theta$ is the parameter), establish a polar coordinate system with the coordinate origin as the pole and the positive half of the $x$-axis as the polar axis. The polar equation of curve $C\_2$ is $\rho =4\sin (\theta +\dfrac{\pi }{3})$, and the Cartesian equation of line $l$ is $y=\dfrac{\sqrt{3}}{3}x$.

(I) Find the polar equations of curve $C\_1$ and line $l$;

(II) Given that line $l$ intersects curves $C\_1$ and $C\_2$ at points $A$ and $B$ respectively, which are different from the pole, and the polar radii of $A$ and $B$ are $\rho\_1$ and $\rho\_2$, find the value of $|\rho\_2-\rho\_1|$.

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