
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 the two foci of an ellipse are $F_{1}(0,-2)$ and $F_{2}(0,2)$, and the ellipse passes through the point $(-\frac{3}{2},\frac{5}{2})$.  
$(1)$ Find the standard equation of the ellipse.  
$(2)$ A line passing through the origin with a slope of $\frac{3}{4}π$ intersects the ellipse at points $A$ and $B$. Find the area of $\triangle ABF_{2}$.

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