
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 an operation $㊉$, if the following conditions are satisfied, then $G$ is called a "harmonious set" with respect to the operation $㊉$:
1. For any $a, b \in G$, $a㊉b \in G$;
2. There exists $e \in G$ such that for all $a \in G$, $a㊉e = e㊉a = a$.
Determine which of the following sets with their respective operations are "harmonious sets".
1. $G = \{$non-negative integers$\}$, $㊉$ is addition of integers;
2. $G = \{$even numbers$\}$, $㊉$ is multiplication of integers;
3. $G = \{$planar vectors$\}$, $㊉$ is addition of planar vectors;
4. $G = \{$quadratic trinomials$\}$, $㊉$ is addition of polynomials.

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