
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 that \( (x_1, y_1) \) and \( (x_2, y_2) \) are two points on the line whose equation is \( y = mx^2 + nx + p \), find the distance between \( (x_1, y_1) \) and \( (x_2, y_2) \) in terms of \( x_1, x_2, m, \) and \( n\).

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