
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 proposition $p$: the equation $x^{2}+2mx+4=0$ has real roots; proposition $q$: the equation $x^{2}+2\left(m-2\right)x-3m+10=0$ has real roots. Given that $p$ and $\neg q$ are both true propositions, find the range of real numbers for $m$.

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