
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
Proposition $p$: The domain of $f(x)= \sqrt{x^{2}+mx+1}$ is $\mathbb{R}$; 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 statement, and "p or q" is a true statement, find the range of the real number $m$.

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