
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 the inequality $ax^{2}+\left(1-2a\right)x-2 \gt 0$, $a\in R$.  
$(1)$ If the solution set of the inequality is $\{x\left|\right.x \lt -1$ or $x \gt 2\}$, find the value of $a$;  
$(2)$ Discuss the solution set of the inequality for $a\in R$.

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