
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 a non-empty set $G$ with operation $⊕$, the set satisfies:

1. For any $a, b ∈ G$, $a ⊕ b ∈ G$;
2. There exists $e ∈ G$ such that for all $a ∈ G$, $a ⊕ e = e ⊕ a = a$.

Then $G$ is called a harmonious set with respect to operation $⊕$.

The following sets and operations are given:

1. $G$ is the set of non-negative integers, $⊕$: addition of real numbers;
2. $G$ is the set of even numbers, $⊕$: multiplication of real numbers;
3. $G$ is the set of all quadratic trinomials, $⊕$: multiplication of polynomials;
4. $G = \{x | x = a + b \sqrt{2}, a, b ∈ Q \}$, $⊕$: multiplication of real numbers;

Which of the following is a harmonious set? (Please fill in the number)

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