
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
$(1)$ Calculate: $|1-\sqrt{3}|-\sqrt{2}\times \sqrt{6}+\frac{1}{{2-\sqrt{3}}}-(\frac{2}{3})^{-2}$;<br/>$(2)$ Given $m$ is a constant less than $0$, solve the system of inequalities with respect to $x$: $\left\{\begin{array}{l}{4x-1>x-7}\\{-\frac{1}{4}x<\frac{3}{2}m-1}\end{array}\right.$.

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