
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 the value of the following expressions:
\\((1)(-0.1)^{0}+ 32 \times 2^{\frac{2}{3}}+ (\frac{1}{4})^{-\frac{1}{2}}\\)
\\((2)\log_{10} 500+\log_{10} \frac{8}{5}- \frac{1}{2}\log_{10} 64+50(\log_{10} 2+\log_{10} 5)^{2}\\)

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