
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
Let points A and B have coordinates (-2, 0) and (2, 0) respectively. Point P is any point on curve C, and the product of the slopes of lines PA and PB is $- \frac {1}{4}$.  
(Ⅰ) Find the equation of curve C;  
(Ⅱ) Draw tangents from point (m, 0) to the circle $x^2+y^2=1$ that intersect curve C at points E and F. When $|m| > 1$, find the maximum value of $|EF|$.

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