
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 $f\left(x\right)=x^{3}-3x^{2}+3$, the following propositions are made:<br/>① The tangent line to the graph of the function $y=f\left(x\right)$ at the point $\left(1,f\left(1\right)\right)$ is $3x+y-4=0$;<br/>② The function $y=f\left(x\right)$ has 3 zeros;<br/>③ The function $y=f\left(x\right)$ attains a maximum value at $x=2$;<br/>④ The graph of the function $y=f\left(x\right)$ is symmetric about the point $\left(1,1\right)$. Determine the correct propositions.

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