
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
Through a point \( P \) on the ellipse \( y^{2} + \frac{x^{2}}{4} = 1 \), draw two tangents to the circle \( x^{2} + y^{2} = 1 \). The line containing the chord of tangency intersects the \( x \)-axis and \( y \)-axis at points \( E \) and \( F \) respectively. What is the minimum area of triangle \( \triangle EOF \)?

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