
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
【Concept Learning】Define a new operation: the operation of taking the quotient of several identical rational numbers (all not equal to $0$) is called division by circles. For example, $2\div 2\div 2$, $\left(-3\right)\div \left(-3\right)\div \left(-3\right)\div \left(-3\right)$, etc. Analogous to the power of rational numbers, we write $2\div 2\div 2$ as $2^{③}$, read as "circle $3$ times of $2$", $\left(-3\right)\div \left(-3\right)\div \left(-3\right)\div \left(-3\right)$ is written as $\left(-3\right)^{④}$, read as "circle $4$ times of $\left(-3\right)$". Generally, we denote $\underbrace{a÷a÷a⋯÷a}_{n个a}$ as $a^{ⓝ}$, read as "$a$ circle $n$ times". Specifically, we define: $a^{①}=a$.<br/>【Preliminary Exploration】(1) Calculate directly: $2023^{②}=$______；<br/>(2) For any positive integer $n$, the correct statements about division by circles are:______; (Fill in the numbers on the line)<br/>$A$. The circle $2$ times of any non-zero number is equal to $1$<br/>$B$. The circle $3$ times of any non-zero number is equal to its reciprocal<br/>$C$. The circle $n$ times of a number is $1$ or $-1$<br/>$D$. The circle odd times of a negative number results in a negative number, and the circle even times of a negative number results in a positive number<br/>【In-depth Thinking】We know that the subtraction operation of rational numbers can be converted into addition operation, and the division operation can be converted into multiplication operation. How can the division by circles operation of rational numbers be converted into power operation?<br/>(3) Write the circle $n$ times of a rational number $a\left(a\neq 0\right)$ in the form of powers: $a^{ⓝ}=$______；<br/>(4) Calculate: $-1^{⑧}-14^{2}\div (-\frac{1}{2})^{④}\times \left(-7\right)^{⑥}$.

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