
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
Discuss the properties of the function $f(x) = e^x - \ln(x+3)$ and determine which of the following properties hold:

1. The function $f(x)$ has a minimum value;
2. There exists a unique critical point $x_0 \in (-1, 0)$;
3. There exists $x_0 \in (-3, +\infty)$ such that $f(x_0) = -1$;
4. For all $x \in (-3, +\infty)$, $f(x) > -\frac{1}{2}$.

List all the correct conclusions by filling in the corresponding serial numbers.

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