
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 angle between two vectors in space $\overrightarrow{AB}=(1,-1,m)$ and $\overrightarrow{AC}=(1,2,m)$ is not greater than $\frac{\pi}{2}$; proposition $q$: The eccentricity $e$ of the hyperbola $\frac{{y}^{2}}{5}- \frac{{x}^{2}}{m}=1$ is in the interval $(1,2)$. If $\neg q$ and $p \land q$ are both false propositions, find the range of the real number $m$.

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