
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
$(1)(-5)+9$;  
$(2)12-(-16)+(-2)-1$;  
$(3)6\div (-2)\times (-\frac{1}{3})$;  
$(4)(-15)\times (\frac{1}{3}+\frac{1}{5})$;  
$(5)(-2)^{3}-(-8)\div |-\frac{4}{3}|$;  
$(6)-1^{2022}-(\frac{1}{2}-\frac{1}{3})\times 3$.

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