
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:  
$(1){(2\frac{7}{9})}^{0.5}+0．{1}^{-2}+{(2\frac{10}{27})}^{-\frac{2}{3}}-3{π}^{0}+\frac{37}{48}$;  
$(2)lo{g}_{2}3•lo{g}_{3}4+{(lg5)}^{2}+lg5•lg20+\frac{1}{2}lg16-{2}^{lo{g}_{2}3}$.

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