
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 $C_{1}: (x- \sqrt {3})^{2}+(y-1)^{2}=4$ is given. With the origin $O$ as the pole and the positive $x$-axis as the polar axis, a polar coordinate system is established. The curve obtained by rotating $C_{1}$ counterclockwise by $\dfrac {π}{6}$ around the pole is denoted as $C_{2}$.
- (Ⅰ) Find the polar equations of the curves $C_{1}$ and $C_{2}$.
- (Ⅱ) The ray $\theta= \dfrac {π}{3}(p > 0)$ intersects the curves $C_{1}$ and $C_{2}$ at points $A$ and $B$, respectively, which are different from the pole $O$. Find $|AB|$.

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