
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 complex number $z=(m^{2}+m-6)+(m^{2}+m-2)i$, where $m\in R$, and the corresponding point in the complex plane is denoted as $A$.  
$(1)$ If the complex number $z-2m$ is purely imaginary, find the value of the real number $m$;  
$(2)$ If point $A$ lies in the second quadrant, determine the range of values for the real number $m$.

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