
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
Simplify and find the value of:<br/>$(1)$ Calculate $\sqrt[3]{{(-4)}^{3}}-{(\frac{1}{2})}^{0}+0.2{5}^{\frac{1}{2}}×{(\frac{-1}{\sqrt{2}})}^{-4}$;<br/>$(2)$ $\frac{{a}^{\frac{2}{3}}\sqrt{b}}{{a}^{\frac{1}{2}}•\sqrt[3]{b}}÷{(\frac{{a}^{-1}\sqrt{{b}^{-1}}}{b\sqrt{a}})}^{\frac{2}{3}}$.

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