
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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