
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) $(-0.1)^0+ 32 \times 2^{ \frac {2}{3}}+ \left( \frac {1}{4} \right)^{- \frac {1}{2}}$  
(2) $\lg 500 + \lg \frac {8}{5} - \frac {1}{2}\lg 64 + 50(\lg 2 + \lg 5)^2.$

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