
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) $(0.001)^{-\frac{1}{3}} + 27^{\frac{2}{3}} + \left(\frac{1}{4}\right)^{-\frac{1}{2}} - \left(\frac{1}{9}\right)^{-1.5}$  
(2) $\frac{1}{2}\lg 25 + \lg 2 - \lg \sqrt{0.1} - \log_{2}9 \cdot \log_{3}2$.

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