
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 triangle has vertices \( (0,0) \), \( (2,2) \), and \( (6m,0) \), and the line \( y = mx \) divides the triangle into two triangles of equal area. What is the sum of all possible values of \( m \)?
**A**) \(-\frac{1}{2}\)  
**B**) \(-\frac{1}{4}\)  
**C**) \(-\frac{1}{3}\)  
**D**) \(0\)  
**E**) \( \frac{1}{3}\)

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