
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
The vertices of a triangle are A(-4, 0), B(2, 4), C(0, 3), and point D is a point on the line containing side AB.
(1) Find the equation of the line $l$ that contains the median to side AB.
(2) If line $l$ is the angle bisector of $\angle ACD$, find the equation of line CD.

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