
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 polar equation of curve $C_1$ as $\rho^2\cos2\theta=8$, and the polar equation of curve $C_2$ as $\theta= \frac {\pi}{6}$, curves $C_1$ and $C_2$ intersect at points A and B.  
(Ⅰ) Find the polar coordinates of points A and B;  
(Ⅱ) 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 segment MN.

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