
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
Given $x$ and $y$ satisfy $\left(x-2\right)^{2}+|y-3|=0$. Simplify and then evaluate the expression: $[\left(x-2y\right)\left(x+2y\right)-\left(x-y\right)^{2}+y\left(y+2x\right)]\div \left(-2y\right)$.

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