
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
$(1)$ Calculate: $-3^{2}+2^{2023}\times (-\frac{1}{2})^{2022}+\left(-2024\right)^{0}$;  
$(2)$ Simplify first, then evaluate: $[\left(x+2y\right)^{2}-\left(2x+y\right)\left(2x-y\right)-5(x^{2}+y^{2})]\div 2x$, where $x=-\frac{1}{2}$, $y=1$.

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