
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
Calculate:  
(1) $\lg 500 + \lg \frac{8}{5} - \frac{1}{2}\lg 64 + \log_{2}3 \cdot \log_{3}4$  
(2) $0.0081^{-\frac{1}{4}} - [3 \times (\frac{7}{8})^{0}]^{-1} \times [81^{-0.25} + (3 \frac{3}{8})^{-\frac{1}{3}}]^{-\frac{1}{2}}.$

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