
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 equation of an ellipse is \\(x^{2}+ \frac{y^{2}}{n}=1(n∈R)\\), with two foci being \\(F\_1\\) and \\(F\_2\\).
(1) If \\(n=-1\\), a line passing through the left focus \\(F\_1\\) with a slope of \\(\sqrt{3}\\) intersects the conic section at points \\(A\\) and \\(B\\). Find the perimeter of \\(\triangle ABF\_2\\).
(2) If \\(n=4\\), \\(P\\) is a point on the conic section. Find the maximum and minimum values of \\(PF\_1 \cdot PF\_2\\).

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