
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 vectors $\overrightarrow{a}$, $\overrightarrow{b}$ satisfy $|\overrightarrow{a}|=2\sqrt{2}|\overrightarrow{b}|\neq 0$, and the function of $x$, $f(x)=2x^{3}+3|\overrightarrow{a}|x^{2}+6\overrightarrow{a}\cdot\overrightarrow{b}x+7$ is monotonically increasing on the set of real numbers $R$, determine the range of the angle between vectors $\overrightarrow{a}$, $\overrightarrow{b}$.

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