
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 plane rectangular coordinate system $(xOy)$, the parametric equations of curve $C_{1}$ are given by $\begin{cases} x=3+3\cos \theta \ y=3\sin \theta \end{cases}$ 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 $\rho= \sqrt {3}\sin \theta+\cos \theta$, and the polar equation of curve $C_{3}$ is $\theta= \dfrac {\pi}{3}$.
(I) Find the polar equation of curve $C_{1}$;
(II) Curve $C_{3}$ intersects with curve $C_{1}$ at points $O$ and $A$, and intersects with curve $C_{2}$ at points $O$ and $B$. Find $|AB|$.

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