
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 the ellipse \(\frac{x^{2}}{9} + \frac{y^{2}}{5} = 1\) and a point \((\sqrt{5}, \sqrt{2})\) inside the ellipse, draw two chords \(AB\) and \(CD\). Tangents to the ellipse at points \(A\) and \(B\) intersect at point \(E\), and tangents to the ellipse at points \(C\) and \(D\) intersect at point \(F\). Find the equation of the line \(EF\).

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