
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 that the equation of a circle is $x^{2}+y^{2}=r^{2}$, the equation of the tangent line passing through a point $M(x_{0},y_{0})$ on the circle is $x_{0}x+y_{0}y=r^{2}$. By analogy, determine the equation of the tangent line passing through a point $P(x_{0},y_{0})$ on the ellipse $\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$.

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