
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 a cubic function $f(x)=x^{3}+bx^{2}+cx+d$ $(a,b,c \in \mathbb{R})$ passes through the point $(3,0)$, and the tangent line of the function $f(x)$ at the point $(0,f(0))$ is exactly the line $y=0$.
$(1)$ Find the expression of the function $f(x)$;
$(2)$ Let the function $g(x)=9x+m-1$, if the function $y=f(x)-g(x)$ has two zeros in the interval $[-2,1]$, find the range of the real number $m$.

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