
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
Calculate:<br/>$(1)$ Calculate: $-\sqrt[3]{-8}-|\sqrt{3}-2|+\sqrt{(-3)^{2}}+(-\sqrt{3})$;<br/>$(2)$ Solve the system of inequalities $\left\{\begin{array}{l}2x+5≤3(x+2)\\ 2x-\frac{1+3x}{2}＜1\end{array}\right.$, and write down the non-negative integer solutions of the system of inequalities.

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