
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 proposition p: The equation $x^2+mx+1=0$ has two distinct real roots, and proposition q: The inequality $x^2-2(m+1)x+m(m+1)>0$ holds for any real number $x$, if "p∨q" is true and "p∧q" is false, find the range of real numbers for $m$.

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