
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
Let $x$, $y$, and $z$ be nonzero real numbers. Determine the minimum value $m$ and the maximum value $M$ of 
\[
\frac{|x + y + z|}{|x| + |y| + |z|}
\]
and compute $M - m.$

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