
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 "$\oplus $": $a\oplus b=2a-ab$, for example, $1\oplus \left(-3\right)=2\times 1-1\times \left(-3\right)=5$. Find the value of:<br/>
$(1)$ $\left(-2\right)\oplus 3$;<br/>
$(2)$ If $\left(-3\right)\oplus x=\left(x+1\right)\oplus 5$, find the value of $x$;<br/>
$(3)$ If $x\oplus 1=2\left(1\oplus y\right)$, find the value of the algebraic expression $\frac{1}{2}x+y+1$.

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