
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 a finite set $A = \{a_1, a_2, a_3, \ldots, a_n\}$ ($n \geq 2$), if the elements $a_i$ ($i = 1, 2, 3, \ldots, n$) satisfy $a_1a_2\ldots a_n = a_1 + a_2 + \ldots + a_n$, then A is called a "Resurrection Set." Consider the following statements:  
1. The set $\left\{\frac{-1 + \sqrt{5}}{2}, \frac{-1 - \sqrt{5}}{2}\right\}$ is a "Resurrection Set."
2. If $a_1, a_2 \in \mathbb{R}$, and $\{a_1, a_2\}$ is a "Resurrection Set," then $a_1a_2 > 4$.
3. If $a_1, a_2 \in \mathbb{N}^{*}$, then $\{a_1, a_2\}$ cannot be a "Resurrection Set."
4. If $a_i \in \mathbb{N}^{*}$, then there is exactly one "Resurrection Set" $A$ with $n = 3$.
Identify the correct conclusions. (Fill in the blank with all the correct conclusion numbers)

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