
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 $": when $a\geqslant b$, $a\oplus b=ab-a$; when $a \lt b$, $a\oplus b=ab+b$.  
$(1)$ Fill in the blank: $(3-\sqrt{3})⊕\sqrt{3}=$______;  
$(2)$ If $2x\oplus \left(x+1\right)=6$, find the value of $x$.

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