
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 sets $A=\{(x,y)|x^{2}+mx-y+2=0, x\in\mathbb{R}\}$ and $B=\{(x,y)|x-y+1=0, x\in\mathbb{R}\}$, find the range of real number $m$ values such that $A\cap B\neq \varnothing$.

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