
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 $f(x)=x^{3}-3x$.

$(1)$ Find the intervals of monotonicity for the function $f(x)$;

$(2)$ If the function $g(x)=f(x)-m$ has three zeros in the interval $\left[-\dfrac{3}{2},3\right]$, find the range of the real number $m$.

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