
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: $\left(-2021\right)^{0}+3\sqrt{27}+(1-3^{-2}\times 18)$;  
$(2)$ Simplify first, then evaluate: $\frac{x^2-y^2}{x^2-2xy+y^2}\cdot \frac{(x-y)(2x+3y)}{x+y}-xy(\frac{2}{x}+\frac{3}{y})$, where $\left(x,y\right)$ are the coordinates of the intersection points of the graphs of the functions $y=2x$ and $y=\frac{2}{x}$.

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