
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
An ellipse with the equation
\[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\]
contains the circles \((x - 2)^2 + y^2 = 1\) and \((x + 2)^2  + y^2 = 1.\) Determine the smallest possible area of the ellipse which can be expressed in the form \(k \pi.\) Find \(k.\)

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