
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) Evaluate the expression $(0.008)^{\frac{1}{3}} + (\sqrt{2} - \pi)^0 - \left(\frac{125}{64}\right)^{-\frac{1}{3}}$.
(2) Simplify and evaluate the expression $\frac{(\log_3 2 + \log_9 2) \cdot (\log_4 3 + \log_8 3)}{\lg 600 - \frac{1}{2}\lg 0.036 - \frac{1}{2}\lg 0.1}$.

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