
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 $M(x_0, y_0)$ on the circle, the equation of the tangent line at point $M$ is $$x_0x + y_0y = R^2$$. By analogy, write down the equation of the tangent line at a point $P(x_0, y_0)$ on the ellipse $$\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \quad (a > b > 0)$$.

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