
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
Determine whether the following functions are odd, even, or neither, and provide the reasoning:<br/>$(1)f(x)={x}^{3}-\frac{1}{x}$;<br/>$(2)f\left(x\right)=|x|,x\in \left[-4,5\right]$;<br/>$(3)f(x)=\left\{\begin{array}{c}{x}^{2}-3x,x＞1\\{x}^{2}+3x,x＜-1\end{array}\right.$.

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