
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 propositions P and Q: Proposition P states that the equation $x^2+mx+1=0$ has two distinct negative real roots. Proposition Q states that the equation $4x^2+4(m-2)x+1=0$ has no real roots. If "P or Q" is true and "P and Q" is false, then the range of real numbers m can take is _______.

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