
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 real numbers $a$, $b$, $c$ satisfying $a \geq b \geq c$, $a+b+c=0$ and $a \neq 0$. Let $x_1$, $x_2$ be the two real roots of the equation $ax^2+bx+c=0$. Then, the maximum distance between points $A(x_1, x_2)$ and $B(x_2, x_1)$ in the Cartesian coordinate system is.

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