
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 \\(P(x_0,y_0)\\) is a point on the parabola \\(y^2=2px(p > 0)\\), the slope of the tangent line at point \\(P\\) can be obtained as follows: Differentiate both sides of \\(y^2=2px\\) with respect to \\(x\\), yielding \\(2yy'=2p\\), thus \\(y'=\frac{p}{y}\\). Therefore, the slope of the tangent line at \\(P\\) is \\(k=\frac{p}{y_0}\\). Similarly, find the equation of the tangent line to the hyperbola \\(x^2-\frac{y^2}{2}=1\\) at point \\(P(\sqrt{2},\sqrt{2})\\) as \_\_\_\_\_\_\_\_\_\_\_.

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