
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: $|\sqrt{5}-3|+(\frac{1}{2})^{-1}-\sqrt{20}+\sqrt{3}\cos 30^{\circ}$;<br/>$(2)$ Solve the system of inequalities: $\left\{\begin{array}{l}{-3(x-2)≥4-x}\\{\frac{1+2x}{3}＞x-1}\end{array}\right.$.

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