
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 $f(x)=x^{3}-3ax-1$ $(a\neq 0)$,

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

$(2)$ If $f(x)$ has an extremum at $x=-1$, and the line $y=m$ intersects the graph of $y=f(x)$ at three distinct points, find the range of values for $m$.

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