
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 $p$: The equation $x^{2}+mx+1=0$ has two distinct real roots, $q$: The inequality $4x^{2}+4(m-2)x+1 > 0$ always holds true over $\mathbb{R}$. If $\neg p$ is true and $p \lor q$ is true, find the range of the real number $m$.

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