
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
Suppose \( m \) and \( k \) are real numbers, and \( mk > 0 \), meaning \( m \) and \( k \) are either both positive or both negative. Which of the following points cannot exist on the line with the equation \( y = mx + k \)?
**A)** \( (0, 2000) \)  
**B)** \( (0, -2000) \)  
**C)** \( (20, 100) \)  
**D)** \( (20, -100) \)  
**E)** \( (2000, 0) \)

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