
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 the following two propositions:  
Proposition $p$: The quadratic equation with real coefficients $x^{2}+mx+2=0$ has imaginary roots;  
Proposition $q$: For the equation $2x^{2}-4(m-1)x+m^{2}+7=0$ ($m\in\mathbb{R}$), the sum of the moduli of its two imaginary roots does not exceed $4\sqrt{2}$,  
If both propositions $p$ and $q$ are true, find the range of the real number $m$.

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