
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 at $(0,0)$, $(2,2)$, and $(8n,0)$. A line given by $y = nx$ divides the triangle into two areas of equal size. Determine the sum of all possible values of $n$.
**A**. $-\frac{1}{4}$  
**B**. $\frac{1}{4}$  
**C**. $-\frac{1}{8}$  
**D**. $\frac{1}{8}$

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