
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) $27^{\frac{2}{3}} - 2^{\log_2 3} \times \log_2 \frac{1}{8}$;  
(2) $\frac{1}{\sqrt{5}-2} - (\sqrt{5}+2)^0 - \sqrt{(2-\sqrt{5})^2}$.

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