
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: $\left(\frac{1}{2}\right)^{3}+(-5)^{0}-\left(-\frac{1}{4}\right)^{-2}$;  
$(2)$ Calculate: $\frac{x(x^{2}y^{2}-xy)-y(x^{2}-x^{3}y)}{2x^{2}y}$.

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