
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:
$$(1) \log_{4} \sqrt{8} + \lg 50 + \lg 2 + 5^{\log_{5} 3} + (-9.8)^{0};$$
$$(2) (\frac{27}{64})^{\frac{2}{3}} - (\frac{25}{4})^{0.5} + (0.008)^{- \frac{2}{3}} \times \frac{2}{5}.$$

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