
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 that the universal set is $R$, set $A=\{x|{x}^{2}-5x+6=0\}$, $B=\{x|{x}^{2}-(m+3)x+{m}^{2}=0\}$, and $A\cup\overline{B}=R$, find the range of real numbers for $m$.

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