
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
The real numbers \( x, y, \) and \( z \) satisfy both of the equations below.

\[
\begin{array}{r}
x + y + z = 2 \\
xy + yz + xz = 0
\end{array}
\]

Let \( a \) be the minimum possible value of \( z \) and \( b \) be the maximum possible value of \( z \). What is the value of \( b - a \)?

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