
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 nor a maximum value;
- ③ The graph of $f(x)$ and its tangent line at $(0,0)$ intersect at two points;
- ④ The graph of $f(x)$ and the line $x - y + 2012 = 0$ intersect at two points.

Among these conclusions, the correct ones are __________.

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