
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, the curve $C_{1}$: $\begin{cases} x=3+3\cos a \\ y=2\sin a \end{cases}$ (where $a$ is a parameter) undergoes a scaling transformation $\begin{cases} x'= \frac {x}{3} \\ y'= \frac {y}{2} \end{cases}$ to become the curve $C_{2}$. A polar coordinate system is established with the origin as the pole and the positive $x$-axis as the polar axis.  
(Ⅰ) Find the polar equation of $C_{2}$.  
(Ⅱ) Suppose the polar equation of curve $C_{3}$ is $\rho\sin \left( \frac {\pi}{6}-\theta\right)=1$, and curve $C_{3}$ intersects with curve $C_{2}$ at points $P$ and $Q$. Find the value of $|PQ|$.

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