
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
(1) $8^{0.25} \times 42 + (32 \times \sqrt{3})^6 + \log_{3}{2} \times \log_{2}(\log_{3}{27})$；
(2) $\dfrac{\lg{8} + \lg{125} - \lg{2} - \lg{5}}{\lg{\sqrt{10}} \lg{0.1}}$.

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