
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
The equation of the tangent line to the circle \\((x-a)^{2}+(y-b)^{2}=r^{2}(r > 0)\\) at point \\(P(x_{0},y_{0})\\) is \\((x_{0}-a)(x-a)+(y_{0}-b)(y-b)=r^{2}\\). By analogy, the equation of the tangent line to the ellipse \\(\dfrac{x^{2}}{a^{2}}+ \dfrac{y^{2}}{b^{2}}=1(a > b > 0)\\) at point \\(P(x_{0},y_{0})\\) is __________.

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