
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 $f(x) = x^{2}e^{x}$ 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 nor a maximum value;  
3. The graph of $f(x)$ intersects its tangent line at $(0,0)$ at two points;  
4. The graph of $f(x)$ intersects 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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