
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/>$(1)-xy^{2}z^{3}\cdot (-x^{2}y)^{3}$;<br/>$(2)-2{a^2}({\frac{1}{2}ab+{b^2}})$;<br/>$(3)[\left(3a+b\right)^{2}-b^{2}]\div a$;<br/>$(4)[\left(x+y\right)^{2}-\left(x-y\right)^{2}]\div 2xy$.

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