
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}\\) is \\(\rho^{2}\cos 2\theta=18\\), and the polar equation of curve \\(C_{2}\\) is \\(\theta= \frac {\pi}{6}\\).
\\((1)\\) Find the polar coordinates of points \\(A\\) and \\(B\\);  
\\((2)\\) 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 \\(|MN|\\).

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