
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/>$(1)-1^{2023}+(2023-π)^{0}+(-\frac{1}{2})^{-2}$;<br/>$(2)(-\frac{1}{2}xy)^{3}•2x(2{x}^{3}{y}^{2})÷(x{y}^{2})^{2}$;<br/>$(3)\left(x-y\right)\left(x+y\right)(x^{2}-y^{2})$;<br/>$(4)[(x+2y)^{2}+(3x+2y)(3x-2y)]÷\frac{1}{2}x$.

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