
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/>$(1)(1\frac{1}{4}-\frac{5}{6}+\frac{1}{2})×(-12)$;<br/>$(2)(-81)÷\frac{9}{4}×\frac{4}{9}÷(-32)$;<br/>$(3)-2^3-3\frac{1}{2}×6-(-5)$;<br/>$(4)-1^{2022}+[1-(1-0.5\times \frac{1}{3})]\times |2-\left(-2\right)^{3}|$.

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