
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
For a polynomial in terms of $y$, when $y$ takes any pair of opposite numbers $n$ and $-n$, if the value of the polynomial is the same, then the polynomial is called an "even polynomial"; if the values of the polynomial are opposite, then the polynomial is called an "odd polynomial." For example, $y^{2}$ is an "even polynomial," and $y^{3}$ is an "odd polynomial."<br/>$(1)$ If the polynomial $A$ is an "odd polynomial" in terms of $y,"$ when $y$ takes $3$ and $-3$, the corresponding values of the polynomial are $A_{1}$ and $A_{2}$, then $A_{1}+A_{2}=\_\_\_\_\_\_.$<br/>$(2)$ Determine whether the expression $\left(y-3\right)^{2}-\left(y+3\right)^{2}$ is an "even polynomial" or an "odd polynomial," and explain the reason.<br/>$(3)$ For the polynomial $y^{5}-y^{3}+y^{2}-y+2$, it can be seen as a sum of an "even polynomial" and an "odd polynomial."<br/>①The "even polynomial" is______ and the "odd polynomial" is______.<br/>②When $y$ takes $-3$, $-2$, $-1$, $0$, $1$, $2$, $3$, the sum of the values of these seven polynomials is______.

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