
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
Given $A=2x^{2}-3xy+y^{2}+2x+2y$, $B=4x^{2}-6xy+2y^{2}-3x-y$.  
$(1)$ When $x=2$, $y=-\frac{1}{5}$, find the value of $B-2A$.  
$(2)$ If $|x-2a|+\left(y-3\right)^{2}=0$, and $B-2A=a$, find the value of $a$.

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