
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
Find the standard equation of the ellipse that satisfies the following conditions:  
\\((1)\\) The foci are on the x-axis, the focal distance is \\(4\\), and it passes through the point \\(P(3,-2 \sqrt {6})\\).  
\\((2)\\) The focal distance is \\(8\\), and the eccentricity is \\(0.8\\).

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