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

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