
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 plane, the trajectory of points whose product of slopes of lines connecting them to two fixed points \\(A_1(0, -a)\\) and \\(A_2(0, a)\\) \\((a > 0)\\) equals a non-zero constant \\(m\\), together with points \\(A_1\\) and \\(A_2\\), forms a curve \\(C\\) that can be a circle, an ellipse, or a hyperbola. Given the following four conclusions:

\\(①\\) When \\(m = -1\\), the curve \\(C\\) is a circle;

\\(②\\) When \\(m = -2\\), the eccentricity of curve \\(C\\) is \\(\dfrac{\sqrt{2}}{2}\\);

\\(③\\) When \\(m = 2\\), the equations of the asymptotes of curve \\(C\\) are \\(y = \pm \dfrac{\sqrt{2}}{2}x\\);

\\(④\\) When \\(m \in (-\infty, -1) \cup (0, +\infty)\\), the coordinates of the foci of curve \\(C\\) are \\(\left(0, -a\sqrt{1 + \dfrac{1}{m}}\right)\\) and \\(\left(0, a\sqrt{1 + \dfrac{1}{m}}\right)\\).

The correct conclusions are \_\_\_\_\_\_\_\_\_\_.

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