
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 curve $C$ is: 
$$
\begin{cases} 
x=1+ \sqrt {7}\cos \theta \\
y= \sqrt {7}\sin \theta 
\end{cases} (\theta \text{ is the parameter})
$$
with $O$ as the pole and the non-negative half-axis of $x$ as the polar axis, establish a polar coordinate system.
- (Ⅰ) Find the polar equation of curve $C$;
- (Ⅱ) Given the line $l_{1}: 2\rho\sin (\theta+ \frac {\pi}{3})- \sqrt {3}=0$, and the ray $l_{2}: \theta= \frac {\pi}{3}(\rho > 0)$ intersects curve $C$ at point $P$, and $l_{2}$ 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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