
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 that $| \vec{a}|=2| \vec{b}|, | \vec{b}|\neq0$, and the function of $x$, $f(x)= \frac {1}{3}x^{3}+ \frac {1}{2}| \vec{a}|x^{2}+ \vec{a}\cdot \vec{b}x$, has an extremum on the real number line, determine the range of the angle between $\vec{a}$ and $\vec{b}$.

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