
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 $f(x)=x^{3}-ax^{2}-3x$.
$(1)$ If $f(x)$ is monotonically increasing on $[1,+\infty)$, find the range of the real number $a$.
$(2)$ If the function $g(x)=f(x)-(a^{2}-3)x+1$ ($a > 0$) has at most two zeros, find the range of the real number $a$.

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