
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 an ellipse C that passes through the point $A(2 \sqrt {6}，2)$, with two foci at $(-2 \sqrt {6}，0)，(2 \sqrt {6}，0)$.
(1) Find the standard equation of ellipse C;
(2) Let line l intersect ellipse C at points A and B, with |AB|=6, find the maximum area of △AOB.

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