
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
Fill in the blank: (Please write the result directly on the line)  
Define a new operation "$\oplus$", for any rational numbers $a$, $b$, we have $a\oplus b=\frac{a+3b}{2}$,  
$(1) 4\left(2\oplus 5\right)=\_\_\_\_\_\_.$  
$(2)$ If $A=x^{2}+2xy+y^{2}$, $B=-2xy+y^{2}$, then $\left(A\oplus B\right)+\left(B\oplus A\right)=\_\_\_\_\_\_.$

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