
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
Find the values of the following expressions:  
(1) ${\log_{9}}\sqrt[3]{27}-{5^{{\log_{25}16}}}+{(\log{2})^2+\log{5}\times\log{20}$;  
(2) ${8^{0.25}}\times\sqrt[4]{2}+{(\sqrt[3]{2}\times\sqrt{3})^6}+{(2\frac{10}{27})^{-\frac{2}{3}}}$.

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