
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 new operation is defined: $a@b = (a+b)^2 - (a-b)^2$. Below are several conclusions about this operation:
1. $1@(-2) = -8$;
2. $a@b = b@a$;
3. If $a@b = 0$, then $a$ must be $0$;
4. If $a+b = 0$, then $(a@a) + (b@b) = 8a^2$.

Among these conclusions, the correct ones are numbered     .

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