
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
It is stipulated that several identical rational numbers (all not equal to $0$) divided by each other are called division powers, such as $2\div 2\div 2$, $\left(-3\right)\div \left(-3\right)\div \left(-3\right)\div \left(-3\right)$, etc. Analogous to the exponentiation of rational numbers, we denote $2\div 2\div 2$ as $2^{③}$, read as "$2$ to the circle $3$ power", $\left(-3\right)\div \left(-3\right)\div \left(-3\right)\div \left(-3\right)$ as $\left(-3\right)^{④}$, read as "$-3$ to the circle $4$ power". Generally, we denote dividing $n$ $a$'s as $a^{ⓝ}$, read as "$a$ to the circle $n$ power". Please read the above material and complete the following questions:  
$(1)$ Write down the results directly: $2^{③}=$______, ${(-\frac{1}{3})}^{④}$______;  
$(2)$ We know that subtraction of rational numbers can be converted to addition, and division can be converted to multiplication; can division powers of rational numbers be converted to exponentiation? We can perform the following calculations:  
For example, ${2}^{④}=2÷2÷2÷2=2×\frac{1}{2}×\frac{1}{2}×\frac{1}{2}={(\frac{1}{2})}^{2}$;  
$(-3)^{⑤}=\left(-3\right)\div \left(-3\right)\div \left(-3\right)\div \left(-3\right)\div \left(-3\right)=(-3)×-(\frac{1}{3})×-(\frac{1}{3})×(-\frac{1}{3})×(-\frac{1}{3})={(-\frac{1}{3})}^{3}$;  
Carefully consider the above calculation process, and write the following results directly in the form of exponents:  
$5^{⑤}=\_\_\_\_\_\_,\left(-2\right)^{⑥}=$______;  
$(3)$ Think about writing the division power of a non-zero rational number $a$ as an exponent: $a^{ⓝ}=$______;  
$(4)$ Calculate: $1{2}^{2}÷{(-\frac{1}{3})}^{④}×{(-2)}^{⑤}$.

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