
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
We define: for any real numbers $a$, $b$, $c$, $d$, $\left[a,b\right]*\left[c,d\right]=ac-bd$, where the right side of the equation represents the usual multiplication and subtraction operations, for example: $\left[3,2\right]*\left[5,1\right]=3\times 5-2\times 1=13$.  
$(1)$ Find the value of $\left[-4,3\right]*\left[2,-6\right]$;  
$(2)$ Given that the equation in terms of $x$, $\left[x,2x-1\right]*\left[mx+1,m\right]=0$, has two real number roots, find the range of values for $m$.

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