
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
Let $P$ be a set of numbers that contains at least two numbers. If for any $a, b \in P$, the operations $a+b$, $a-b$, $ab$, and $\frac{a}{b}$ (with $b \neq 0$) are also in $P$, then $P$ is called a field. For example, the set of rational numbers $Q$ is a field; the set $F = \{a + b\sqrt{2} | a, b \in Q\}$ is also a field. Consider the following statements:

① The set of integers is a field;  
② If the set of rational numbers $Q \subseteq M$, then the set $M$ must be a field;  
③ A field must be an infinite set;  
④ There are infinitely many fields.  
Among these statements, the correct ones are \_\_\_\_\_\_ . (Fill in the blanks with the numbers of the statements you believe are correct.)

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