
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 a circle $C:x^{2}+y^{2}=r^{2}$ and a point $M(x_{0},y_{0})$ outside the circle, the tangent lines $MA$ and $MB$ are drawn from $M$ to the circle, with $A$ and $B$ being the points of tangency. The equation of $AB$ is $x_{0}x+y_{0}y=r^{2}$. By analogy, for an ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1 (a > b > 0)$ and a point $M(x_{0},y_{0})$ outside the ellipse, if tangent lines $MA$ and $MB$ are drawn from $M$ to the ellipse with $A$ and $B$ as the points of tangency, the equation of $AB$ is ________.

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