
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
A function that possesses the property $f\left( \frac{1}{x} \right) = -f(x)$ is referred to as satisfying the "negative inversion" property. Among the following functions:
1. $y = x - \frac{1}{x}$
2. $y = x + \frac{1}{x}$
3. $y = \begin{cases}
     x, & 0 < x < 1 \\
     0, & x = 1 \\
     -\frac{1}{x}, & x > 1
\end{cases}$

Which ones satisfy the "negative inversion" property?

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