
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:

$(1)\ (\frac{1}{4})^{-\frac{1}{2}} \times \frac{(\sqrt{4ab^{-1}})^3}{(0.1)^{-2}(a^3b^{-3})^{\frac{1}{2}}}$;

$(2)\ \frac{\log_{10} 8 + \log_{10} 125 - \log_{10} 2 - \log_{10} 5}{\log_{10} \sqrt{10} \cdot \log_{10} 0.1}$.

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