
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 that the function $y=f(x)$ is an increasing function defined on the interval $[a, b]$, where $a, b \in \mathbb{R}$, and $0 < b < -a$. Let the function $F(x) = f^2(x) - f^2(-x)$, and $F(x)$ is not identically zero. Then, regarding $F(x)$, the following statements are made:  
① The domain is $[-b, b]$  
② It is an odd function  
③ The minimum value is 0  
④ It is monotonically increasing within its domain  
Among these statements, the correct ones are \_\_\_\_\_\_. (Write down all the correct serial numbers)

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