
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
Let $a$ and $b$ be real numbers. Define an operation $@$ as follows: $a@b=\left(a+b\right)^{2}-\left(a-b\right)^{2}$. Then the following conclusions are given:<br/>① If $a@b=0$, then $a=0$ or $b=0$;<br/>② $a@\left(b+c\right)=a@b+a@c$;<br/>③ There are no real numbers $a$ and $b$ that satisfy $a@b=a^{2}+5b^{2}$;<br/>④ Let $a$ and $b$ be the length and width of a rectangle. If the perimeter of the rectangle is fixed, then when $a=b$, $a@b$ is maximized. The correct conclusions are ____.

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