
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 $a$, $b$ be nonzero real numbers. Calculate the maximum and minimum values of 
\[\frac{3|a + b|}{|a| + |b|},\]
and find $M - m$ where $m$ and $M$ respectively represent the minimum and maximum values of the above expression.

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