
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
Consider the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$ with left and right foci $F_1$ and $F_2$. A line $l$ passes through $F_1$ and intersects the ellipse at points $A$ and $B$.

(1) Calculate the perimeter of triangle $\Delta ABF_2$;

(2) If the slope of line $l$ is $\frac{\pi}{4}$, calculate the area of triangle $\Delta ABF_2$.

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