
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 division operation involving several identical non-zero rational numbers is called a "division power," such as $2\div 2\div 2$, $0.8\div 0.8\div 0.8$, etc. By analogy with exponentiation for rational numbers, we denote $2\div 2\div 2$ as $2^{③}$, read as "the 3rd division power of 2"; $\left(-5\right)\div \left(-5\right)\div \left(-5\right)\div \left(-5\right)$ is denoted as $\left(-5\right)^{④}$ and read as "the 4th division power of -5". In general, $a\div a\div a\ldots \div a$ (with $n$ occurrences of $a$, where $a\neq 0$) is called "$a$ to the power of n division." Regarding division powers, the following statements are correct: 

① The 2nd division power of any non-zero number is equal to 1;  
② The 3rd division power of any non-zero number is equal to its reciprocal;  
③ $3^{⑥}=6^{③}$;  
④ The division power of a negative number is negative for odd powers and positive for even powers.

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