
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
Among the following propositions, the correct ones are __________.  
① If $x \in \mathbb{R}$, then $x^2 \in \mathbb{R}$  
② If $x^2 \in \mathbb{R}$, then $x \in \mathbb{R}$  
③ If $x_1 + y_1i = x_2 + y_2i$ ($x_1, x_2, y_1, y_2 \in \mathbb{C}$), then $x_1 = x_2$ and $y_1 = y_2$  
④ If $x_1 = x_2$ and $y_1 = y_2$, then $x_1 + y_1i = x_2 + y_2i$ ($x_1, x_2, y_1, y_2 \in \mathbb{C}$)

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