
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:

(1) $(0.027)^{\frac{2}{3}} +\left( \frac{27}{125} \right)^{-\frac{1}{3}} -\left( 2\frac{7}{9} \right)^{0.5}$；

(2) $\left( \frac{1}{4} \right)^{-\frac{1}{2}} \cdot \frac{(\sqrt{4ab^{-1}})^{3}}{(0.1)^{-1}\cdot(a^{3}\cdot b^{-3})^{\frac{1}{2}} }$．

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