
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
A non-empty set $G$ with respect to operation $\oplus$ satisfies:  
(1) For any $a, b \in G$, $a+b \in G$;  
(2) There exists $e \in G$ such that for all $a \in G$, $a \oplus e = e \oplus a = a$,  
then $G$ is called a harmonious set with respect to operation $\oplus$.  
Now, consider the following sets and operations:  
① $G$ is the set of non-negative integers, $\oplus$: addition of real numbers;  
② $G$ is the set of even numbers, $\oplus$: multiplication of real numbers;  
③ $G$ is the set of all quadratic trinomials, $\oplus$: multiplication of polynomials;  
④ $G=\{x|x=a+b\sqrt{2}, a, b \in \mathbb{Q}\}$, $\oplus$: multiplication of real numbers;  
Among these, the ones that are harmonious sets are \_\_\_\_\_\_ (Please fill in the numbers)

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