
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 $p$: $f(x)=\frac{2}{x-m}$ is a decreasing function in the interval $(1,+\infty)$; proposition $q$: $x_{1}$, $x_{2}$ are the two real roots of the equation $x^{2}-ax-2=0$, and the inequality $m^{2}+5m-3\geqslant |x_{1}-x_{2}|$ holds for any real number $a\in[-1,1]$. If $\neg p \wedge q$ is true, find the range of the real number $m$.

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