
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
An ellipse $E$ passes through the point $A(2,3)$, with its axes of symmetry coinciding with the coordinate axes. Its foci, $F\_1$ and $F\_2$, are located on the $x$-axis, and the eccentricity $e=\frac{1}{2}$.

(1) Find the equation of the ellipse $E$;
(2) Find the equation of the line that bisects the angle $\angle F\_1AF\_2$.

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