
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 following propositions: ① $3.14 \in \mathbb{Q}$; ② $\{0\} = \emptyset$; ③ $a \in \{a, b\}$; ④ $(1, 2) \in \{y | y = x + 1\}$; ⑤ $\{x | x^2 + 1 = 0, x \in \mathbb{R}\} \subseteq \{1\}$. Among these, the correct propositions are.

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