
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
Given a function $f(x)=\frac{{a}^{2}-a}{{x}^{2}}-\frac{3}{x}$, where $a\in R$.  
$(1)$ When $a=2$, find the solution set of the inequality $f\left(x\right) \gt -1$;  
$(2)$ If the inequality $f(x)＜\frac{6}{{x}^{3}}$ holds for $x\in \left(0,1\right]$, find the set of integer values of $a$.

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