
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 a line $\sqrt {6}x+2y-2 \sqrt {6}=0$ passes through a vertex E and a focus F of the ellipse $\frac {x^{2}}{a^{2}}+ \frac {y^{2}}{b^{2}}=1$ ($a>b>0$),
(1) Find the standard equation of the ellipse;
(2) Find the equation of the tangent line to the ellipse passing through point P($\sqrt {5}$, $\sqrt {3}$).

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