
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
A hyperbola E passes through the point A(4, 6), has its axes aligned with the coordinate axes, and its foci F<sub>1</sub> and F<sub>2</sub> lie on the X-axis. The eccentricity e of the hyperbola is 2.  
(1) Find the equation of the hyperbola E;  
(2) Find the equation of the line containing the angle bisector of ∠F<sub>1</sub>AF<sub>2</sub>.

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