
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: $2\sin 60^{\circ}-\left(\pi -2\right)^{0}+(\frac{1}{3})^{-2}+|1-\sqrt{3}|$;<br/>$(2)$ Solve the inequality system: $\left\{\begin{array}{l}{\frac{1}{2}x+1＜\frac{3}{2}}\\{1-5(x+1)≤6}\end{array}\right.$.

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