
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 $a$ and $b$ be nonzero real numbers. Let $m'$ and $M'$ be the minimum value and maximum value of
\[\frac{|a + b|}{|a| + |b|},\]
respectively. Calculate $M' - m'$ where $a = \frac{1}{2}$ and $b = -\frac{1}{2}$ for the minimum, and $a = 3, b = 3$ for the maximum.

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