
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 hyperbola E has its center at the origin, with F(3,0) as one of its foci. A line l passes through F and intersects the hyperbola at points A and B. The midpoint of line segment AB is N(-12,-15). Find the equation of the hyperbola E.

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