
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 as follows: $a@b=(a+b)^{2}-(a-b)^{2}$. 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 \_\_\_\_\_\_ .

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