
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
If the function $y=f(x)$ defined on $R$ satisfies that there exist a finite number of non-zero independent variable values $x_{0}$ such that $f(-x_{0})=-f(x_{0})$, then $y=f(x)$ is called a class odd function. If the function $y=x^{4}+(a^{2}-1)x^{2}+a\sin x$ is a class odd function, then the range of real number $a$ is ____.

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