
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 ratio of the major axis to the focal distance of an ellipse is 2:1, the left focus is F(-2,0), and a certain point is P(-8,0).

1. Find the standard equation of the ellipse E;
2. A line passing through P intersects the ellipse at points P1 and P2. Find the maximum area of triangle P1F2F and the slope of the line when this occurs.

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