
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 circle $C$ is $\begin{cases} & x=1+\cos \varphi \\ & y=\sin \varphi \end{cases}$ ($\varphi$ is the parameter). Establish a polar coordinate system with $O$ as the pole and the non-negative semi-axis of $x$ as the polar axis.

(I) Find the polar equation of circle $C$;

(II) The polar equation of line $l$ is $2\rho \sin (\theta +\dfrac{\pi }{3})=3\sqrt{3}$, the intersection points of ray $OM: \theta =\dfrac{\pi }{3}$ with circle $C$ are $O,P$, and with line $l$ is $Q$, find the length of segment $PQ$.

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