
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 that $F\_1$ and $F\_2$ are the left and right foci of the ellipse $(E)$: $\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1 (a > b > 0)$, $M$ and $N$ are the endpoints of its minor axis, and the perimeter of the quadrilateral $MF\_1NF\_2$ is $4$, let line $(l)$ pass through $F\_1$ intersecting $(E)$ at points $A$ and $B$ with $|AB|=\frac{4}{3}$.

1. Find the maximum value of $|AF\_2| \cdot |BF\_2|$.
2. If the slope of line $(l)$ is $45^{\circ}$, find the area of $\triangle ABF\_2$.

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