
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 $f\left(x\right)=\left(x-1\right)^{2}e^{x}$, which of the following conclusions is correct?  
① The function $f\left(x\right)$ has a root;  
② The function $f\left(x\right)$ has both a maximum and a minimum value;  
③ The function $f\left(x\right)$ has neither a maximum nor a minimum value;  
④ The graph of the function $f\left(x\right)$ intersects the line $y=1$ at 3 points.

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