
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 $f(x)=(x^2-3)e^x$, the following conclusions are presented:
1. $f(x)$ has a local minimum but no global minimum.
2. $f(x)$ has a local maximum but no global maximum.
3. If the equation $f(x)=b$ has exactly one real root, then $b > 6e^{-3}$.
4. If the equation $f(x)=b$ has exactly three distinct real roots, then $0 < b < 6e^{-3}$.

Among these conclusions, the correct ones are __________.

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