
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/>$(1)(-3x^{2}y)^{2}\cdot (2xy^{2})\div (-6x^{3}y^{4})$;<br/>$(2)\left(x+2\right)\left(x-3\right)-x\left(x-1\right)$;<br/>$(3)2024\times 2022-2023^{2}($calculate using multiplication formula);<br/>$(4)(-\frac{1}{2})^{-2}-\left(3.14-\pi \right)^{0}-8^{2024}\times \left(-0.125\right)^{2023}$.

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