
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
Let the function $y=f(x)$ have its tangent line equation at any point $(x_{0},y_{0})$ on its graph as $y-y_{0}=(3x_{0}^{2}-6x_{0})(x-x_{0})$, and $f(3)=0$. Then, the solution set of the inequality $\frac{x-1}{f(x)}\geqslant 0$ is ______.

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