
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
A student was studying the properties of the function $f(x) = x^2e^x$ and came to the following conclusions:  
① The interval where $f(x)$ is monotonically decreasing is $(-2, 0)$;  
② $f(x)$ has neither a minimum value nor a maximum value;  
③ The graph of $f(x)$ intersects with its tangent line at $(0, 0)$ at two points;  
④ The graph of $f(x)$ intersects with the line $x-y+2012=0$ at two points.  
Among these conclusions, the correct ones are numbered     .

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