
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 conclusion that the equation of the tangent line at point $P(x_0, y_0)$ on the circle ${x^{2}}+{{y}^{2}}={{r}^{2}}(r > 0)$ is $\frac{x_{0}x}{{r}^{2}}+ \frac{y_{0}y}{{r}^{2}}=1$, use analogy to find the equation of the tangent line at point $P(x_0, y_0)$ on the ellipse $\frac{{{x}^{2}}}{{{a}^{2}}}+\frac{{{y}^{2}}}{{{b}^{2}}}=1(a > b > 0)$.

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