
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 $m\in R$, proposition $p$: the equation $x^{2}-mx+m=0$ has two distinct real roots in $(1,+\infty)$; proposition $q$: the function $f(x)=\frac{1}{4{x}^{2}+mx+m}$ is defined for all real numbers.  
$(1)$ If proposition $p$ is true, find the range of real number $m$:  
$(2)$ If exactly one of propositions $p$ and $q$ is true, find the range of real number $m$.

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