
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) $\left(\frac{9}{16}\right)^{\frac{1}{2}} + 31000 - \left(\frac{64}{27}\right)^{-\frac{1}{3}} + 3 \cdot e^0$;  
(2) $\frac{\lg \sqrt{27} + \lg 8 - \log_{4}8}{\frac{1}{2}\lg 0.3 + \lg 2}$;  
(3) $\lg^2 5 + \lg 2 \cdot \lg 50$.

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