
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
Let proposition $p: f(x)= \sqrt{x^{2}+mx+1}$ have a domain of $\mathbb{R}$; proposition $q$: the equation $\frac{x^{2}}{m}+\frac{y^{2}}{2}=1$ represents an ellipse with foci on the $y$-axis. If "p and q" is a false proposition, and "p or q" is a true proposition, find the range of the real number $m$.

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