
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 center of an ellipse is at the origin of the coordinate system, one focus is at $F\_1(0,-1)$, and the eccentricity is $\frac{\sqrt{3}}{3}$.

(1) Find the standard equation of the ellipse.
(2) A line passing through $F\_1$ 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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