
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
Evaluate and simplify:

1. $\dfrac{ \sqrt{a^{3}b^{2} \sqrt[3]{ab^{2}}}}{(a^{ \frac{1}{4}}b^{ \frac{1}{2}})^{4}a^{- \frac{1}{3}}b^{ \frac{1}{3}}}$ ($a > 0,b > 0$);

2. $\left( \left. - \dfrac{27}{8} \right. \right)^{- \frac{2}{3}} +(0.002)- \dfrac{1}{2}-10( \sqrt{5}-2)^{-1}+(\sqrt{2}- \sqrt{3})^{0}$;

3. $\dfrac{5}{6}a^{ \frac{1}{3}} \cdot b^{-2}\cdot(-3a- \dfrac{1}{2}b^{-1})÷(4a^{ \frac{2}{3}} \cdot b^{-3})^{ \frac{1}{2}}$.

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