
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 the parabola $y = ax^2 + bx + c$ and points $(x_1, y_1)$ and $(x_2, y_2)$ on the parabola, where $a$, $b$, $c$, $x_1$, and $x_2$ are given, find the distance between the two points.

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