
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 and evaluate the following expressions:

$(1) {(0.008)}^{\frac{1}{3}} + {(\sqrt{2} - \pi)}^{0} - {\left( \frac{125}{64} \right)}^{-\frac{1}{3}} $

$(2) \frac{({{\log }_{3}}2+{{\log }_{9}}2) \cdot ({{\log }_{4}}3+{{\log }_{8}}3)}{\log 600-\frac{1}{2}\log 0.036-\frac{1}{2}\log 0.1} $

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