
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 a triangle △ABC with vertices A(4, 4), B(-4, 2), and C(2, 0):
1. Find the equation of the line on which the median CD of side AB lies;
2. Find the equation of the altitude from vertex C to side AB;
3. Find the coordinates of the centroid G of triangle ABC.

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