
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 universal set $U=\{-4,-1,0,1,2,4\}$, $M=\{x\in \mathbb{Z} | 0 \leqslant x < 3\}$, $N=\{x|x^{2}-x-2=0\}$,  
$(1)$ Find sets $M$ and $N$;  
$(2)$ If the set $\{m^{2}, m-2\} = \overline{U}(M \cup N)$, find the value of the real number $m$.

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