
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
The left and right foci of the hyperbola \\(x^{2}- \frac{y^{2}}{b^{2}}=1\\) (where \\(b > 0\\)) are denoted as \\(F_1\\) and \\(F_2\\), respectively. A line \\(l\\) passes through \\(F_2\\) and intersects the hyperbola at points \\(A\\) and \\(B\\).

\\((1)\\) If the inclination angle of \\(l\\) is \\(\frac{\pi}{2}\\), and \\(\triangle F_1AB\\) is an equilateral triangle, find the equation of the asymptotes of the hyperbola;

\\((2)\\) Let \\(b= \sqrt{3}\\). If the slope of \\(l\\) exists and the length of \\(AB\\) is 4, find the slope of \\(l\\).

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