
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 \( y \) be a nonzero real number and \( k \) a positive constant. Determine the maximum and minimum values of
\[
\frac{|k \cdot y + y|}{|k \cdot y| + |y|}
\]
and compute \( M - m \), where \( M \) and \( m \) are the maximum and minimum values, respectively.

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