
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
) Find the range of values for the area of triangle $ABF_2$, where $F_1$ is a point on the ellipse $C$, and line $l$ intersects the ellipse at point $A$. Given that $\overrightarrow{AF_{1}}=λ \overrightarrow{F_{1}B}$, where $λ∈[2]$.

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