
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 or calculate the following expressions:
1. $\frac{{({a}^{\frac{2}{3}}{b}^{-1})}^{-\frac{1}{2}}{a}^{-\frac{1}{2}}{b}^{\frac{1}{3}}}{\sqrt[6]{a{b}^{5}}}$;
2. ${(0.027)}^{\frac{2}{3}}+{(\frac{27}{125})}^{-\frac{1}{3}}-{(2\frac{7}{9})}^{0.5}$.

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