
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 formula $\cos 3\theta =4\cos ^{3}\theta -3\cos \theta $, $\theta \in R$, with the help of this formula, we can find the range of the function $f\left(x\right)=4x^{3}-3x-2(x\in [0$,$\frac{\sqrt{3}}{2}])$. Then the range of this function is ____.

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