
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:<br/>$(1)4x^2(x-\frac{1}{4})$;<br/>$(2)\left(y+1\right)^{2}-\left(y+2\right)\left(y-2\right)$;<br/>$(3)\frac{8{a}^{2}{b}^{4}}{{c}^{4}{d}^{2}}\div (-\frac{2a{b}^{3}}{{c}^{2}d})^{2}$;<br/>$(4)\frac{{x}^{2}+4x+4}{x+1}\div (x-1-\frac{3}{x+1})$;<br/>$(5)(4\sqrt{10}-3\sqrt{6}$）$÷\frac{\sqrt{2}}{2}$;<br/>$(6)\sqrt{8}+(\sqrt{2}+3)(\sqrt{2}-5)$.

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