
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
Calculate the difference between the roots of the following equation.

$$
x^{2}-2\left(a^{2}+b^{2}+c^{2}-2 a c\right) x+\left(b^{2}-a^{2}-c^{2}+2 a c\right)^{2}=0
$$

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