
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
1. Compute: $(1)(\log_{5}3+\log_{ \sqrt{5}}9)(\log_{3}5-\log_{9}5)+\sqrt[6]{(1- \sqrt{2})^{6}}\times0.{25}^{0.5}$
2. Given $2^{x}-2^{-x}=2$, find the value of $\frac{(8^{x}+8^{-x})(4^{x}+4^{-x}-2)}{16^{x}-16^{-x}}$.

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