
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. Simplify and then evaluate the expression: $(1)(2x+y)(2x-y)-4x(x-y)$, where $x=\frac{1}{2}$, $y=-1$;
2. Simplify and then evaluate the expression: $\frac{x^{2}}{x-y}-\frac{y^{2}}{x-y}$, where $x=1+2\sqrt{3},y=1-2\sqrt{3}$;
3. Simplify and then evaluate the expression: $\frac{x^{2}-9}{x^{2}+8x+16}\div\frac{x-3}{x+4}-\frac{x}{x+4}$, where $x=\sqrt{7}-4$.

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