
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
The derivative of a function $y=f(x)$ defined on $R$ is denoted as $f′(x)$. If there exists $x_{0}∈[a,b]$ such that $f(b)-f(a)=f′(x_{0})(b-a)$ holds, then $x_{0}$ is called the "mean value point" of the function $f(x)$ on the interval $[a,b]$. Find the "mean value point" of the function $f(x)=x^{3}-3x$ on the interval $[-2,2]$.

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