
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 the right focus of the ellipse $C$: $\frac{x^{2}}{a^{2}}+ \frac{y^{2}}{b^{2}}=1(a > b > 0)$ is $(\sqrt{5},0)$, and the eccentricity is $\frac{\sqrt{5}}{3}$.
(1) Find the standard equation of the ellipse $C$;
(2) If the moving point $P(x_{0},y_{0})$ is outside the ellipse $C$, and the two tangents from point $P$ to the ellipse $C$ are perpendicular to each other, find the trajectory equation of point $P$.

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