
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
A circle given by the equation $({x-a})^{2}+({y-b})^{2}=r^{2}$ $(r < 0)$ has a tangent line at point $P(x_{0},y_{0})$ with equation $(x_{0}-a)(x-a)+(y_{0}-b)(y-b)=r^{2}$. By analogy, find the equation of the tangent line to the ellipse given by $\frac{{x}^{2}}{{a}^{2}}+\frac{{y}^{2}}{{b}^{2}}=1$ $(a > b > 0)$ at point $P(x_{0},y_{0})$.

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