
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 $x^{2}+ \frac{y^{2}}{n}=1$ ($n\in R$), and its two foci are labeled $F_1$ and $F_2$:
1. If $n=-1$, find the perimeter of triangle $\triangle ABF_2$, where a line with a slope of $\sqrt{3}$ passes through the left focus $F_1$ and intersects the conic at points $A$ and $B$.
2. If $n=4$, for a point $P$ on the conic, find the maximum and minimum values of the product $PF_1 \cdot PF_2$.

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