
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 polar coordinate system, it is known that the polar equation of curve C₁ is $ρ^2\cos2θ=8$, and the polar equation of curve C₂ is $θ = \frac{π}{6}$. The two curves C₁ and C₂ intersect at points A and B. Using the pole O as the origin and the line of the polar axis as the x-axis, a Cartesian coordinate system is established. It is known that the parametric equation of line l is 
$$
\begin{cases} 
x=1+ \frac{\sqrt{3}}{2}t \\
y=\frac{1}{2}t 
\end{cases}
$$
($t$ is the parameter).
(1) Find the polar coordinates of points A and B.
(2) Curve C₁ intersects line l at points M and N. Find the length of segment MN.

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