
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
For the function $f\left(x\right)=x^{3}-ax^{2}$, the following four statements are given:<br/>① For any $a\in R$, $f\left(x\right)$ has extremum;<br/>② The slope of the tangent line of the curve $y=f\left(x\right)$ cannot be less than $-\frac{{{a^2}}}{3}$;<br/>③ For any $a\in R$, the curve $y=f\left(x\right)$ has two tangent lines parallel to the line $y=x-1$;<br/>④ There exists $a\in R$ such that the curve $y=f\left(x\right)$ has only one tangent line parallel to the line $y=x-1.<br/>The correct statement numbers are ____.

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