
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
Given the curve $C_{1}$ with the polar equation $\rho^{2}\cos 2\theta=8$, and the curve $C_{2}$ with the polar equation $\theta= \frac {\pi}{6}$, the curves $C_{1}$ and $C_{2}$ intersect at points $A$ and $B$.  
(Ⅰ) Find the polar coordinates of points $A$ and $B$;  
(Ⅱ) The curve $C_{1}$ intersects with the line $\begin{cases} x=2+ \frac { \sqrt {3}}{2}t \\ y= \frac {1}{2}t \end{cases}$ (where $t$ is a parameter) at points $M$ and $N$, respectively. Find the length of the segment $MN$.

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