
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: $\left(-1\right)^{2023}+18\div (-\frac{1}{3})^{-2}-\sqrt{\frac{3}{2}}\times \sqrt{6}$;<br/>$(2)$ Find all integer solutions of the inequality system $\left\{\begin{array}{l}{4-3x>-x,}\\{1+\frac{x}{2}>-\frac{1}{3}}\end{array}\right.$.

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