
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 the following expressions:<br/>
$(1){(0.027)}^{\frac{2}{3}}+{(\frac{27}{125})}^{-\frac{1}{3}}-{(2\frac{7}{9})}^{\frac{1}{2}}$;<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