
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 following expressions:

1. $(2 \dfrac{7}{9})^{ \frac{1}{2}} -(2 \sqrt{3}-\pi)^{0}-(2 \dfrac{10}{27})^{- \frac{2}{3}} +0.25^{- \frac{3}{2}}$;

2. $\log_{3} \dfrac{ \sqrt[4]{27}}{3}+\lg 25+\lg 4+7^{\log 72}$;

3. $27^{ \frac{2}{3}} -2^{\log 23}\times\log_{2} \dfrac{1}{8}+\log_{2}3\times\log_{3}4$;

4. $\dfrac{1}{ \sqrt{0.25}}+( \dfrac{1}{27})^{- \frac{1}{3}} + \sqrt{(\lg 3)^{2}-\lg 9+1}-\lg \dfrac{1}{3}+{{81}^{0.5{{\log }_{3}}5}}$.

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