
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) $$\log_{2}24 + \log_{10}\frac{1}{2} - \log_{3}\sqrt{27} + \log_{10}2 - \log_{2}3$$
(2) $$\left(33 \times \sqrt{2}\right)^6 - \left(\frac{1}{9}\right)^{-\frac{3}{2}} - (-8)^{0}$$.

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