
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 equation of curve $C$ is: $(x-1)^{2}+y^{2}=1$. Establish a polar coordinate system with $O$ as the pole and the non-negative half-axis of $x$ as the polar axis.  
(Ⅰ) Find the polar equation of curve $C$;  
(Ⅱ) The polar equation of line $l_{1}$ is $2ρ\sin (\theta+ \dfrac {π}{3})+3 \sqrt {3}=0$, and line $l_{2}$: $\theta= \dfrac {π}{3}(\rho∈R)$ intersects curve $C$ at points $O$ and $P$, and intersects line $l_{1}$ at point $Q$. Find the length of segment $PQ$.

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