
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 negative real roots; proposition $q$: The equation $4x^{2}+4(m-2)x+1=0$ has no real roots.  
$(1)$ If "$\neg p$" is a false proposition, find the range of $m$;  
$(2)$ If "$p$ or $q$" is a true proposition, and "$p$ and $q$" is a false proposition, find the range of $m$.

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