
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
Among the following statements: ①$0.09$ is the square root of $0.81$; ②The square root of $-9$ is $\pm 3$; ③The arithmetic square root of $\left(-5\right)^{2}$ is $-5$; ④$\sqrt{-2}$ is a negative number; ⑤The opposite and reciprocal of $0$ are both $0$; ⑥$\sqrt{4}=\pm 2$; ⑦If the cube root of a number is the number itself, then the number is $1$ or $0$; ⑧All real numbers correspond one-to-one with points on the number line. The correct statements are ____.

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