
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
Simplify or evaluate:  
(1) $(2 \frac{4}{5})^{0} + 2^{-2} \times (2 \frac{1}{4})^{- \frac{1}{2}} - (\frac{8}{27})^{ \frac{1}{3}}$  
(2) $2(\lg \sqrt{2})^{2} + \lg \sqrt{2} \cdot \lg5 + \sqrt{(\lg \sqrt{2})^{2} - \lg2 + 1}$.

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