
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
In evaluating a quadratic equation, one student makes an error in the constant term and finds 3 and 7 as roots. Another student makes an error in the coefficient of the linear term and finds roots 5 and -1. What was the correct equation?
**A)** \(x^2 - 10x - 5 = 0\)  
**B)** \(x^2 + 10x + 5 = 0\)  
**C)** \(x^2 - 10x + 5 = 0\)  
**D)** \(x^2 - 10x + 15 = 0\)  
**E)** \(x^2 + 5x - 10 = 0\)

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