
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 equation
\[\frac{x^2}{4a^2} + \frac{y^2}{4b^2} = 1\]
contains the circles \((x - 2)^2 + y^2 = 4\) and \((x + 2)^2 + y^2 = 4.\) Find the smallest possible area of the ellipse that can be expressed in the form \(k \pi.\)

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