
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 operator "$*$" as follows: $a*b=ab+\frac{3}{b}-\sqrt{3}$. For example, $({-2})*1=({-2})×1+\frac{3}{1}-\sqrt{3}=1-\sqrt{3}$. Find the values of:<br/>
$(1)$ $\sqrt{27}*3$;<br/>
$(2)$ $({\sqrt{12}+\sqrt{3}})*\sqrt{12}$;<br/>
$(3)$ If $x*({-\sqrt{3}})=\sqrt{3}$, find the value of $x$.

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