
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:

$(1) \ 0.027 - \frac{1}{3} - \left(\frac{1}{7}\right)^{-2} + \left(2\frac{7}{9}\right)^{\frac{1}{2}} - (\sqrt{2} - 1)^0$;

$(2) \ \left(\begin{matrix} \frac{5}{6}a^{\frac{1}{3}} \\ b^{-2} \end{matrix}\right) \cdot (-3a - \frac{1}{2}b^{-1}) \div (4a^{\frac{2}{3}} b^{-3})^{\frac{1}{2}} \cdot \sqrt{ab}$.

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