
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 the following:<br/>$(1)(π-3)^0+(\frac{1}{2})^{-3}-3^2+(-1)^{2024}$.<br/>$(2)3m•2n^2-(2n)^2•\frac{1}{2}m$.<br/>$(3)$Simplify first, then evaluate: $[\left(x+2y\right)^{2}-y\left(x+3y\right)+\left(x-y\right)\left(x+y\right)]\div \left(2x\right)$, where $x=-3$,$y=2$.

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