
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) $8^{0.25} \times 4\sqrt{2} + 2^{log_{\sqrt{2}}3} + \log_{(2+ \sqrt{3})}(\sqrt{3} - 2)^2$  
(2) Given $a + a^{-1} = 3$, find the value of $\frac{a^2 + a^{-2} - 2}{a^3 + a^{-3} - 3}$.

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