
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:

$(1){(2\frac{4}{5})^{0}}+{{2}^{-2}}\times {{(2\frac{1}{4})}^{-{\frac{1}{2}}}}-{{(\frac{8}{27})}^{{\frac{1}{3}}}}$ ;

$(2)2{{(\log _{10}\sqrt{2})}^{2}}+\log _{10}\sqrt{2}\cdot \log _{10}5+\sqrt{{{(\log _{10}\sqrt{2})}^{2}}-\log _{10}2+1}$

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