
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 an ellipse with its center at the origin, one of the foci is at $F_1(0, -1)$, and its eccentricity is $\frac{\sqrt{3}}{3}$.  
(1) Find the standard equation of the ellipse;  
(2) A line passing through point $F_1$ intersects the ellipse at points A and B. $F_2$ is the other focus of the ellipse. Find the range of values for the area of $\triangle ABF_{2}$.

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