
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 function $f\left(x\right)=x^{3}-12x+12$.  
$(1)$ Find the extreme values of $f\left(x\right)$;  
$(2)$ Find the maximum and minimum values of $f\left(x\right)$ on the interval $\left[-3,4\right]$;  
$(3)$ If the tangents to the curve $f\left(x\right)$ at points $A$ and $B$ are parallel, write down the coordinates of the midpoint of $A$ and $B$ (just write down the result).

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