
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 $x$ and $y$ be nonzero real numbers, and let $k$ be any real number except 0. Consider $m$ and $M$ the minimum value and maximum value of
\[ \frac{|kx + y|}{|kx| + |y|}. \]
Find $M - m$.

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