
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/>$(1)\left(\pi -2\right)^{0}-|8|+(\frac{1}{3})^{-2}$;<br/>$(2)\left(2x\right)^{3}\cdot (-3xy^{2})\div (-2x^{2}y^{2})$;<br/>$(3)\left(4-x\right)^{2}-\left(x-2\right)\left(x+3)$;<br/>$(4)125^{2}-124\times 126$. (Please use simplified calculations)

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