
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 function $f(x)=mx^{2}-mx-1$.  
$(1)$ If $m=\frac{1}{2}$, solve the inequality: $f(x) \lt 0$;  
$(2)$ If $m\in R$, solve the inequality in terms of $x$: $f(x) \lt (m-1)x^{2}+2x-2m-1$.

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