
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
Define a new operation: $a\&b=b^{2}-ab$, for example, $\left(-2\right)\&3=3^{2}-\left(-2\right)\times 3$.  
$(1)(+\frac{2}{3})\&(-\frac{1}{2})$;  
$(2)$ If $|x+1|+\left(y-3\right)^{2}=0$, find the value of $x\&y$.

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