
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: $\sqrt[3]{-8}-\sqrt{2}+(\sqrt{3})^2+|1-\sqrt{2}|-(-1)^{2023}$;<br/>$(2)$ Solve the equation: $\left\{\begin{array}{l} \frac{1}{2}x-\frac{3}{2}y=-1 \\ 2x+y=3 \end{array}\right.$.

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