
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) $2^{\log_{2}\frac{1}{4}} + \left(\frac{64}{27}\right)^{-\frac{1}{3}} + \log_{5}3 \cdot (\log_{3}10 - \log_{3}2)$;  
(2) $8^{-\frac{1}{3}} + \log_{3}\frac{1}{27} + \log_{6}5 \cdot (\log_{5}2 + \log_{5}3) + 10^{\log_{10}3}$.

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