
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}- \dfrac{y^{2}}{b^{2}} =1(b > 0)\\) are \\(F_{1}\\) and \\(F_{2}\\), respectively. The line \\(l\\) passes through \\(F_{2}\\) and intersects the hyperbola at points \\(A\\) and \\(B\\).

\\((1)\\) The inclination angle of line \\(l\\) is \\( \dfrac{π}{2} \\), and \\(\triangle F_{1}AB\\) 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 \\(( \overrightarrow{F_{1}A} + \overrightarrow{F_{1}B} )\cdot \overrightarrow{AB} =0\\), find the slope of \\(l\\).

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