
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 rectangular coordinate system $(xOy)$, the parametric equation of circle $C$ is given by $\begin{cases} x=1+\cos \phi \\ y=\sin \phi \end{cases} (\phi \text{ is the parameter}).$ Establish a coordinate system with $O$ as the pole and the non-negative half of the $x$-axis as the polar axis.
1. Find the polar equation of circle $C$.
2. If the polar equation of line $l$ is $2\rho\sin (θ+ \frac {π}{3})=3 \sqrt {3}$, and the intersection points of the ray $\sqrt {3}x-y=0(x\geqslant 0)$ with circle $C$ are $O$ and $P$, while its intersection point with line $l$ is $Q$, find the length of line segment $PQ$.

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